Here we go through Dunfield's list of exceptional fillings of the SnapPy census manifolds and check which fillings gives the best bounds on volt. We order the lists by volume and by type.
import snappy
import csv
import time
exceptional_fillings=[]
with open('exceptional_fillings.csv', 'r') as file:
reader = csv.reader(file)
for row in reader:
exceptional_fillings.append(row)
len(exceptional_fillings)
205823
exceptional_fillings[0]
['name', 'kind', 'regina_name', 'betti', 'tree', 'HFhat', 'H1_order', 'L_space', 'unfilled_betti', 'toroidal', 'slope_length', 'cusped', 'slope']
def better_volume(M,index=100,try_hard=False):
'''Computes the verified volume. Returns 0 if SnapPy could not do it.'''
count=0
while count<index:
try:
return M.volume(verified=True)
except:
M.randomize()
count=count+1
if try_hard==True:
pos_triang=find_positive_triangulations(M,number=index,tries=index)
for X in pos_triang:
vol=better_volume(X,index)
if vol!=0:
return vol
return 0
volt=[] #Has elements [regina_name,type,volt,realizing_manifold,realizing_slope]
start_time=time.time()
for x in exceptional_fillings[1:]:
K=snappy.Manifold(x[-2])
vol=better_volume(K,try_hard=True)
volt.append([x[2],x[1],vol,x[-2],x[-1]])
print('Time taken:',(time.time()-start_time)/60,'minutes')
Time taken: 44.25289129018783 minutes
len(volt)
205822
First we sort the list by types.
start_time=time.time() #Sort by type first
volt.sort(key=lambda x: (x[1],x[0],x[2],x[3]))
print('Time taken:',(time.time()-start_time)/60,'minutes')
Time taken: 0.009987910588582357 minutes
start_time=time.time()
volt_new=[]
mfds=[]
for x in volt:
if x[0] not in mfds:
mfds.append(x[0])
volt_new.append(x)
else:
for z in volt_new:
if z[0]==x[0]:
break
if x[2].overlaps(z[2]):
volt_new.append(x)
print('Time taken:',(time.time()-start_time)/60,'minutes')
Time taken: 12.15973523457845 minutes
len(volt_new)
31316
volt_new
[['S2 x S1', 'S2 x S1', 3.252908048472?, 'm043', '(1, 0)'],
['S3', 'S3', 2.0298832128193?, 'm004', '(1, 0)'],
['L(10,3) # L(3,1)', 'connect_sum', 5.185799900161?, 't02780', '(1, 0)'],
['L(10,3) # L(4,1)', 'connect_sum', 6.18183384980?, 'o9_16449', '(1, 0)'],
['L(10,3) # RP3', 'connect_sum', 4.847540571634?, 'v0944', '(0, 1)'],
['L(10,3) # S2 x S1', 'connect_sum', 7.15751736545?, 'o9_28605', '(1, 0)'],
['L(11,2) # L(3,1)', 'connect_sum', 5.21117868644?, 'o9_06327', '(1, 0)'],
['L(11,2) # RP3', 'connect_sum', 4.792929746977?, 't01542', '(1, 1)'],
['L(11,3) # L(3,1)', 'connect_sum', 5.21061582789?, 't02799', '(1, 0)'],
['L(11,3) # L(4,1)', 'connect_sum', 6.20825236737?, 'o9_16838', '(1, 0)'],
['L(11,3) # RP3', 'connect_sum', 4.844905060974?, 'v0941', '(-1, 1)'],
['L(11,3) # S2 x S1', 'connect_sum', 7.17542592163?, 'o9_28950', '(1, 0)'],
['L(12,5) # L(3,1)', 'connect_sum', 5.23666364961?, 't02848', '(1, 0)'],
['L(12,5) # L(4,1)', 'connect_sum', 6.23163870503?, 'o9_17176', '(1, 0)'],
['L(12,5) # RP3', 'connect_sum', 4.853685190922?, 'v0957', '(1, 1)'],
['L(12,5) # S2 x S1', 'connect_sum', 7.19376448987?, 'o9_29265', '(1, 0)'],
['L(13,2) # RP3', 'connect_sum', 4.87257521805?, 'o9_03419', '(1, 1)'],
['L(13,3) # L(3,1)', 'connect_sum', 5.24528268505?, 'o9_06385', '(1, 0)'],
['L(13,3) # RP3', 'connect_sum', 4.935918472254?, 't02014', '(0, 1)'],
['L(13,5) # L(3,1)', 'connect_sum', 5.249121992679?, 't02874', '(1, 0)'],
['L(13,5) # L(4,1)', 'connect_sum', 6.24964219006?, 'o9_17431', '(1, 0)'],
['L(13,5) # RP3', 'connect_sum', 4.900229202632?, 'v1018', '(1, 1)'],
['L(13,5) # S2 x S1', 'connect_sum', 7.21651590661?, 'o9_29685', '(1, 0)'],
['L(14,3) # L(3,1)', 'connect_sum', 5.25754728403?, 'o9_06414', '(1, 0)'],
['L(14,3) # RP3', 'connect_sum', 4.93513219690?, 't02011', '(-1, 1)'],
['L(15,4) # L(3,1)', 'connect_sum', 5.26728743323?, 'o9_06442', '(1, 0)'],
['L(15,4) # RP3', 'connect_sum', 4.97356119408?, 't02177', '(1, 0)'],
['L(16,3) # RP3', 'connect_sum', 4.98135177799?, 'o9_03986', '(0, 1)'],
['L(16,7) # L(3,1)', 'connect_sum', 5.27973466388?, 'o9_06494', '(1, 0)'],
['L(16,7) # RP3', 'connect_sum', 4.94611153041?, 't02055', '(1, 1)'],
['L(17,3) # RP3', 'connect_sum', 4.98105642468?, 'o9_03981', '(1, 1)'],
['L(17,4) # RP3', 'connect_sum', 4.99593317821?, 'o9_04152', '(1, 0)'],
['L(17,5) # L(3,1)', 'connect_sum', 5.28216052115?, 'o9_06509', '(1, 0)'],
['L(17,5) # RP3', 'connect_sum', 4.966109616492?, 't02149', '(-1, 1)'],
['L(18,5) # L(3,1)', 'connect_sum', 5.28756155771?, 'o9_06536', '(1, 0)'],
['L(18,5) # RP3', 'connect_sum', 4.982733969163?, 't02223', '(1, 1)'],
['L(19,4) # RP3', 'connect_sum', 5.011629338472?, 'o9_04400', '(1, 0)'],
['L(19,7) # L(3,1)', 'connect_sum', 5.29352521357?, 'o9_06593', '(1, 0)'],
['L(19,7) # RP3', 'connect_sum', 4.986238235230?, 't02245', '(-1, 1)'],
['L(20,9) # RP3', 'connect_sum', 4.99120921725?, 'o9_04104', '(1, 1)'],
['L(21,8) # L(3,1)', 'connect_sum', 5.30099039446?, 'o9_06662', '(1, 0)'],
['L(21,8) # RP3', 'connect_sum', 5.00845267672?, 't02352', '(1, 1)'],
['L(22,5) # RP3', 'connect_sum', 5.01030988513?, 'o9_04377', '(1, 1)'],
['L(23,5) # RP3', 'connect_sum', 5.018066524666?, 'o9_04505', '(-1, 1)'],
['L(23,7) # RP3', 'connect_sum', 5.01298799095?, 'o9_04424', '(1, 1)'],
['L(24,7) # RP3', 'connect_sum', 5.03550035450?, 'o9_04737', '(1, 0)'],
['L(25,7) # RP3', 'connect_sum', 5.038413861106?, 'o9_04774', '(1, 0)'],
['L(25,9) # RP3', 'connect_sum', 5.02209002929?, 'o9_04581', '(1, 1)'],
['L(26,7) # RP3', 'connect_sum', 5.02737789184?, 'o9_04654', '(1, 1)'],
['L(27,8) # RP3', 'connect_sum', 5.03569743868?, 'o9_04738', '(1, 1)'],
['L(29,12) # RP3', 'connect_sum', 5.03733069775?, 'o9_04764', '(1, 1)'],
['L(29,8) # RP3', 'connect_sum', 5.04010578715?, 'o9_04794', '(-1, 1)'],
['L(3,1) # L(3,1)', 'connect_sum', 3.821687586180?, 'm160', '(0, 1)'],
['L(3,1) # L(4,1)', 'connect_sum', 4.415332477454?, 'm294', '(1, 0)'],
['L(3,1) # L(5,1)', 'connect_sum', 4.737290226750?, 's432', '(1, 0)'],
['L(3,1) # L(5,2)', 'connect_sum', 4.784994925975?, 's458', '(1, 0)'],
['L(3,1) # L(6,1)', 'connect_sum', 4.921482848286?, 'v1045', '(1, 0)'],
['L(3,1) # L(7,1)', 'connect_sum', 5.033712726702?, 't02469', '(1, 0)'],
['L(3,1) # L(7,2)', 'connect_sum', 5.032272571604?, 'v1157', '(1, 0)'],
['L(3,1) # L(8,1)', 'connect_sum', 5.10627180354?, 'o9_05590', '(1, 0)'],
['L(3,1) # L(8,3)', 'connect_sum', 5.111166587521?, 'v1213', '(1, 0)'],
['L(3,1) # L(9,2)', 'connect_sum', 5.14954879165?, 't02736', '(1, 0)'],
['L(3,1) # RP3', 'connect_sum', 2.666744783449?, 'm010', '(-1, 1)'],
['L(3,1) # RP3 # RP3', 'connect_sum', 8.17368069116?, 'o9_41447', '(1, 0)'],
['L(3,1) # S2 x S1', 'connect_sum', 5.333489566898?, 's784', '(1, 0)'],
['L(3,1) # SFS [S2: (2,1) (2,1) (2,-1)]',
'connect_sum',
6.70131362849?,
't09524',
'(1, 0)'],
['L(3,1) # SFS [S2: (2,1) (2,1) (3,-2)]',
'connect_sum',
7.56235887025?,
'o9_34789',
'(1, 0)'],
['L(30,11) # RP3', 'connect_sum', 5.04341473070?, 'o9_04842', '(1, 1)'],
['L(31,12) # RP3', 'connect_sum', 5.04165865727?, 'o9_04815', '(1, 1)'],
['L(34,13) # RP3', 'connect_sum', 5.049343942805?, 'o9_04911', '(-1, 1)'],
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's781', '(1, 0)'],
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's786', '(1, 0)'],
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2229', '(1, 0)'],
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2230', '(1, 0)'],
['L(4,1) # L(5,2)', 'connect_sum', 5.635677579294?, 'v2158', '(1, 0)'],
['L(4,1) # L(6,1)', 'connect_sum', 5.866445349336?, 't05624', '(1, 0)'],
['L(4,1) # L(6,1)', 'connect_sum', 5.86644534934?, 't05625', '(1, 0)'],
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035200?, 'o9_13333', '(1, 0)'],
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035201?, 'o9_13334', '(1, 0)'],
['L(4,1) # L(7,2)', 'connect_sum', 5.991641331038?, 't06330', '(1, 0)'],
['L(4,1) # L(8,3)', 'connect_sum', 6.076894918993?, 't06756', '(1, 0)'],
['L(4,1) # L(9,2)', 'connect_sum', 6.13692901607?, 'o9_15723', '(1, 0)'],
['L(4,1) # RP3', 'connect_sum', 3.6638623767089?, 'm135', '(0, 1)'],
['L(4,1) # RP3', 'connect_sum', 3.6638623767089?, 'm135', '(1, 0)'],
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3219', '(1, 0)'],
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3221', '(1, 0)'],
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3228', '(1, 0)'],
['L(4,1) # SFS [S2: (2,1) (2,1) (2,-1)]',
'connect_sum',
7.20904858752?,
'o9_29531',
'(1, 0)'],
['L(5,1) # L(5,1)', 'connect_sum', 5.97824056586?, 't06263', '(1, 0)'],
['L(5,1) # L(5,2)', 'connect_sum', 5.92748467357?, 't06018', '(1, 0)'],
['L(5,1) # L(6,1)', 'connect_sum', 6.16849439804?, 'o9_16254', '(1, 0)'],
['L(5,1) # L(7,2)', 'connect_sum', 6.281296150787?, 'o9_17910', '(1, 0)'],
['L(5,1) # L(8,3)', 'connect_sum', 6.371755379809?, 'o9_18790', '(1, 0)'],
['L(5,1) # RP3', 'connect_sum', 4.177751073190?, 'm234', '(1, 0)'],
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09262', '(1, 0)'],
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09263', '(1, 0)'],
['L(5,2) # L(5,2)', 'connect_sum', 6.070906691077?, 't06721', '(1, 0)'],
['L(5,2) # L(6,1)', 'connect_sum', 6.10523111916?, 'o9_15244', '(1, 0)'],
['L(5,2) # L(7,2)', 'connect_sum', 6.261399529783?, 'o9_17622', '(1, 0)'],
['L(5,2) # L(8,3)', 'connect_sum', 6.353927376185?, 'o9_18645', '(1, 0)'],
['L(5,2) # RP3', 'connect_sum', 3.853455901405?, 'm168', '(1, 1)'],
['L(5,2) # S2 x S1', 'connect_sum', 6.551743287888?, 'v3382', '(1, 0)'],
['L(6,1) # RP3', 'connect_sum', 4.464658911549?, 's299', '(1, 0)'],
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23974', '(1, 0)'],
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23976', '(1, 0)'],
['L(7,1) # RP3', 'connect_sum', 4.63643309583?, 'v0651', '(1, 0)'],
['L(7,2) # RP3', 'connect_sum', 4.39667280194?, 's235', '(-1, 1)'],
['L(7,2) # S2 x S1', 'connect_sum', 6.92737711231?, 't10606', '(1, 0)'],
['L(8,1) # RP3', 'connect_sum', 4.745944843325?, 't01447', '(1, 0)'],
['L(8,3) # RP3', 'connect_sum', 4.627755634195?, 's391', '(-1, 1)'],
['L(8,3) # S2 x S1', 'connect_sum', 7.03552145709?, 't11090', '(1, 0)'],
['L(9,1) # RP3', 'connect_sum', 4.81954043421?, 'o9_02936', '(1, 0)'],
['L(9,2) # RP3', 'connect_sum', 4.65617065828?, 'v0699', '(1, 1)'],
['L(9,2) # S2 x S1', 'connect_sum', 7.08479003676?, 'o9_27464', '(1, 0)'],
['RP3 # RP3', 'connect_sum', 3.663862376709?, 'm136', '(1, 0)'],
['RP3 # RP3 # RP3', 'connect_sum', 7.94057924779?, 'o9_39343', '(1, 0)'],
['RP3 # S2 x S1', 'connect_sum', 5.074708032049?, 'm410', '(1, 0)'],
['RP3 # SFS [S2: (2,1) (2,1) (2,-1)]',
'connect_sum',
5.495793565063?,
'v1859',
'(1, 0)'],
['RP3 # SFS [S2: (2,1) (2,1) (2,1)]',
'connect_sum',
6.60182141805?,
'o9_21441',
'(0, 1)'],
['RP3 # SFS [S2: (2,1) (2,1) (3,-1)]',
'connect_sum',
6.60182141805?,
'o9_21441',
'(1, 0)'],
['RP3 # SFS [S2: (2,1) (2,1) (3,-2)]',
'connect_sum',
6.33060716016?,
't07829',
'(0, 1)'],
['RP3 # SFS [S2: (2,1) (2,1) (4,-3)]',
'connect_sum',
6.73293177126?,
'o9_22828',
'(0, 1)'],
['RP3 # SFS [S2: (2,1) (3,1) (3,-2)]',
'connect_sum',
7.23745512448?,
'o9_30054',
'(1, 0)'],
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12062', '(1, 0)'],
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12063', '(1, 0)'],
['S2 x S1 # SFS [S2: (2,1) (2,1) (2,-1)]',
'connect_sum',
7.94057924778?,
'o9_39345',
'(1, 0)'],
['SFS [S2: (2,1) (2,1) (10,-1)]',
'finite',
4.24456648431?,
'o9_00899',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,-3)]',
'finite',
4.056860224237?,
'm200',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,-7)]',
'finite',
4.266155248548?,
's171',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,13)]',
'finite',
4.687503062639?,
'o9_02019',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (10,17)]',
'finite',
4.706465607527?,
'o9_02223',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (10,23)]',
'finite',
4.962773185422?,
't02123',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,27)]',
'finite',
4.989521534972?,
'o9_04076',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,3)]',
'finite',
4.36827844030?,
'o9_00934',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,33)]',
'finite',
4.99741873755?,
'o9_04171',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (10,37)]',
'finite',
5.13340799239?,
'o9_05915',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (10,7)]',
'finite',
4.395157815044?,
'o9_01061',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-2)]',
'finite',
3.471287882780?,
's007',
'(-2, 1)'],
['SFS [S2: (2,1) (2,1) (11,-3)]',
'finite',
4.143224022865?,
'm228',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-4)]',
'finite',
4.082091386106?,
'm211',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-5)]', 'finite', 4.11370643634?, 's125', '(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-6)]',
'finite',
4.19140097084?,
'v0230',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-7)]',
'finite',
4.257505232137?,
's168',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-8)]',
'finite',
4.303759395480?,
's191',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,-9)]',
'finite',
4.334569800817?,
'v0291',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,13)]',
'finite',
4.68451284133?,
't01207',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,14)]',
'finite',
4.69228198120?,
'o9_02063',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,15)]',
'finite',
4.69778841952?,
'o9_02107',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,16)]',
'finite',
4.911174350884?,
't01933',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,17)]',
'finite',
4.950882197260?,
't02076',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,18)]',
'finite',
4.70816469042?,
'o9_02262',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,19)]',
'finite',
4.710370094338?,
'o9_02298',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,2)]', 'finite', 3.52916280051?, 'v0006', '(2, 1)'],
['SFS [S2: (2,1) (2,1) (11,20)]',
'finite',
4.90677579446?,
'o9_03573',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,24)]',
'finite',
4.94519589123?,
'o9_03747',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,25)]',
'finite',
5.024722199071?,
't02422',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,26)]',
'finite',
4.997703653139?,
't02297',
'(1, 1)'],
['SFS [S2: (2,1) (2,1) (11,27)]',
'finite',
5.01112155455?,
'o9_04391',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,28)]',
'finite',
5.05199555549?,
'o9_04947',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,29)]',
'finite',
5.02578206864?,
'o9_04631',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,3)]',
'finite',
4.37357574371?,
'o9_00949',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,30)]',
'finite',
5.05171724192?,
'o9_04943',
'(0, 1)'],
['SFS [S2: (2,1) (2,1) (11,31)]',
'finite',
5.160776801323?,
'o9_06139',
'(-1, 1)'],
['SFS [S2: (2,1) (2,1) (11,36)]',
'finite',
5.05918369220?,
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['SFS [S2: (2,1) (3,1) (3,1) (3,-4)]',
'seifert_tor',
7.7462745463?,
'o9_37079',
'(0, 1)'],
['SFS [S2: (2,1) (3,1) (3,1) (3,-5)]',
'seifert_tor',
7.78099915281?,
'o9_37540',
'(-1, 1)'],
['SFS [S2: (2,1) (3,1) (6,-5)]',
'seifert_tor',
3.470395731439?,
'v0003',
'(1, 1)'],
['SFS [S2: (2,1) (4,1) (4,-3)]',
'seifert_tor',
4.180583792452?,
's137',
'(1, 1)'],
['SFS [S2: (3,1) (3,1) (3,-2)]',
'seifert_tor',
4.234647808566?,
'm253',
'(0, 1)'],
['SFS [T: (1,1)]', 'seifert_tor', 6.551743287888?, 't08868', '(1, 0)'],
['SFS [T: (1,2)]', 'seifert_tor', 7.51768989648?, 'o9_34169', '(1, 0)'],
['A x S1 / [ -1,-2 | 5,11 ]',
'torus_bundle',
4.63643309583?,
'v0651',
'(-1, 1)'],
['A x S1 / [ -1,-2 | 6,13 ]',
'torus_bundle',
4.745944843325?,
't01447',
'(1, 1)'],
['A x S1 / [ -1,-2 | 7,15 ]',
'torus_bundle',
4.81954043421?,
'o9_02936',
'(1, 1)'],
['A x S1 / [ -1,-3 | 4,13 ]',
'torus_bundle',
5.17067407823?,
'v1277',
'(-1, 1)'],
['A x S1 / [ -1,-3 | 5,16 ]',
'torus_bundle',
5.38057698908?,
't03264',
'(1, 1)'],
['A x S1 / [ -1,-3 | 6,19 ]',
'torus_bundle',
5.51125439819?,
'o9_07705',
'(1, 1)'],
['A x S1 / [ -1,-4 | 4,17 ]',
'torus_bundle',
5.57360911284?,
't03911',
'(-1, 1)'],
['A x S1 / [ -1,-4 | 5,21 ]',
'torus_bundle',
5.81118022031?,
'o9_10405',
'(1, 1)'],
['A x S1 / [ -1,3 | 6,-17 ]',
'torus_bundle',
5.35704214682?,
'v1577',
'(1, 1)'],
['A x S1 / [ -1,3 | 7,-20 ]',
'torus_bundle',
5.49564840141?,
't03611',
'(-1, 1)'],
['A x S1 / [ -1,3 | 8,-23 ]',
'torus_bundle',
5.58636160767?,
'o9_08190',
'(-1, 1)'],
['A x S1 / [ -1,4 | 6,-23 ]',
'torus_bundle',
5.86644534934?,
't05626',
'(-1, 1)'],
['A x S1 / [ -1,4 | 7,-27 ]',
'torus_bundle',
5.99291035200?,
'o9_13332',
'(-1, 1)'],
['A x S1 / [ -1,5 | 5,-24 ]',
'torus_bundle',
5.97824056586?,
't06264',
'(-1, 1)'],
['A x S1 / [ -1,5 | 6,-29 ]',
'torus_bundle',
6.16849439804?,
'o9_16253',
'(-1, 1)'],
['A x S1 / [ -2,-5 | 11,28 ]',
'torus_bundle',
6.54773701822?,
'o9_20834',
'(0, 1)'],
['A x S1 / [ -2,-5 | 9,23 ]',
'torus_bundle',
6.38127808256?,
't08063',
'(0, 1)'],
['A x S1 / [ -2,-7 | 7,25 ]',
'torus_bundle',
6.64490644348?,
't09252',
'(-1, 1)'],
['A x S1 / [ -2,-7 | 9,32 ]',
'torus_bundle',
6.95449723936?,
'o9_25673',
'(0, 1)'],
['A x S1 / [ -3,-7 | 11,26 ]',
'torus_bundle',
6.79862567957?,
't10011',
'(0, 1)'],
['A x S1 / [ -3,-7 | 14,33 ]',
'torus_bundle',
7.04487690630?,
'o9_26852',
'(0, 1)'],
['A x S1 / [ -3,-8 | 13,35 ]',
'torus_bundle',
7.27943507980?,
'o9_30767',
'(1, 0)'],
['A x S1 / [ -3,8 | 14,-37 ]',
'torus_bundle',
7.18613966342?,
't11614',
'(0, 1)'],
['A x S1 / [ -3,8 | 17,-45 ]',
'torus_bundle',
7.41698819956?,
'o9_32801',
'(0, 1)'],
['A x S1 / [ -4,-11 | 13,36 ]',
'torus_bundle',
7.42631541712?,
'o9_32935',
'(0, 1)'],
['A x S1 / [ -4,-9 | 15,34 ]',
'torus_bundle',
7.19353002805?,
'o9_29257',
'(0, 1)'],
['A x S1 / [ -5,-12 | 17,41 ]',
'torus_bundle',
7.853469097890?,
'o9_38401',
'(1, 0)'],
['A x S1 / [ -5,-13 | 18,47 ]',
'torus_bundle',
8.11485074311?,
'o9_40950',
'(1, 0)'],
['A x S1 / [ -5,12 | 23,-55 ]',
'torus_bundle',
7.98211951766?,
'o9_39739',
'(1, 0)'],
['A x S1 / [ 0,1 | 1,-10 ]',
'torus_bundle',
3.4761739893?,
'o9_00000',
'(-2, 1)'],
['A x S1 / [ 0,1 | 1,-9 ]',
'torus_bundle',
3.43454088591?,
't00000',
'(-2, 1)'],
['A x S1 / [ 0,1 | 1,10 ]',
'torus_bundle',
3.47617398924?,
'o9_00001',
'(2, 1)'],
['A x S1 / [ 0,1 | 1,8 ]',
'torus_bundle',
3.37759740823?,
'v0001',
'(-2, 1)'],
['A x S1 / [ 0,1 | 1,9 ]',
'torus_bundle',
3.434540885903?,
't00001',
'(2, 1)'],
['A x S1 / [ 1,-2 | 6,-13 ]',
'torus_bundle',
4.74594484333?,
't01448',
'(-1, 1)'],
['A x S1 / [ 1,-2 | 7,-15 ]',
'torus_bundle',
4.81954043421?,
'o9_02935',
'(-1, 1)'],
['A x S1 / [ 1,-3 | 5,-16 ]',
'torus_bundle',
5.38057698908?,
't03265',
'(0, 1)'],
['A x S1 / [ 1,-3 | 6,-19 ]',
'torus_bundle',
5.51125439819?,
'o9_07704',
'(0, 1)'],
['A x S1 / [ 1,-4 | 4,-17 ]',
'torus_bundle',
5.57360911283?,
't03910',
'(0, 1)'],
['A x S1 / [ 1,-4 | 5,-21 ]',
'torus_bundle',
5.81118022031?,
'o9_10404',
'(0, 1)'],
['A x S1 / [ 1,3 | 6,17 ]',
'torus_bundle',
5.35704214682?,
'v1578',
'(-1, 1)'],
['A x S1 / [ 1,3 | 7,20 ]',
'torus_bundle',
5.49564840141?,
't03610',
'(1, 1)'],
['A x S1 / [ 1,3 | 8,23 ]',
'torus_bundle',
5.58636160767?,
'o9_08191',
'(1, 1)'],
['A x S1 / [ 1,4 | 6,23 ]',
'torus_bundle',
5.86644534934?,
't05625',
'(0, 1)'],
['A x S1 / [ 1,4 | 7,27 ]',
'torus_bundle',
5.99291035200?,
'o9_13333',
'(0, 1)'],
['A x S1 / [ 1,5 | 6,29 ]',
'torus_bundle',
6.16849439804?,
'o9_16254',
'(0, 1)'],
['A x S1 / [ 2,-5 | 11,-28 ]',
'torus_bundle',
6.54773701822?,
'o9_20833',
'(0, 1)'],
['A x S1 / [ 2,-5 | 7,-18 ]',
'torus_bundle',
6.105653653969?,
'v2899',
'(0, 1)'],
['A x S1 / [ 2,-5 | 9,-23 ]',
'torus_bundle',
6.38127808256?,
't08064',
'(0, 1)'],
['A x S1 / [ 2,-7 | 7,-25 ]',
'torus_bundle',
6.64490644348?,
't09253',
'(0, 1)'],
['A x S1 / [ 2,-7 | 9,-32 ]',
'torus_bundle',
6.95449723936?,
'o9_25672',
'(0, 1)'],
['A x S1 / [ 3,-7 | 11,-26 ]',
'torus_bundle',
6.79862567957?,
't10012',
'(0, 1)'],
['A x S1 / [ 3,-7 | 14,-33 ]',
'torus_bundle',
7.04487690630?,
'o9_26851',
'(0, 1)'],
['A x S1 / [ 3,-8 | 10,-27 ]',
'torus_bundle',
6.951839008429?,
't10729',
'(0, 1)'],
['A x S1 / [ 3,-8 | 13,-35 ]',
'torus_bundle',
7.27943507980?,
'o9_30764',
'(0, 1)'],
['A x S1 / [ 3,11 | 14,51 ]',
'torus_bundle',
7.78220180572?,
'o9_37558',
'(0, 1)'],
['A x S1 / [ 3,8 | 17,45 ]',
'torus_bundle',
7.41698819956?,
'o9_32805',
'(0, 1)'],
['A x S1 / [ 4,-9 | 15,-34 ]',
'torus_bundle',
7.19353002805?,
'o9_29256',
'(0, 1)'],
['A x S1 / [ 5,-13 | 18,-47 ]',
'torus_bundle',
8.1148507431?,
'o9_40949',
'(1, 0)'],
['A x S1 / [ 5,12 | 23,55 ]',
'torus_bundle',
7.98211951766?,
'o9_39740',
'(1, 0)'],
['T x I / [ -10,-3 | -3,-1 ]',
'torus_bundle',
4.813819186104?,
's463',
'(-1, 1)'],
['T x I / [ -11,-7 | -3,-2 ]',
'torus_bundle',
5.133548425107?,
's639',
'(1, 1)'],
['T x I / [ -11,-8 | -4,-3 ]',
'torus_bundle',
5.333489566898?,
's786',
'(-1, 1)'],
['T x I / [ -13,-5 | -5,-2 ]',
'torus_bundle',
5.62537824957?,
's891',
'(-1, 1)'],
['T x I / [ -13,-8 | -8,-5 ]',
'torus_bundle',
6.089649638458?,
's960',
'(1, 0)'],
['T x I / [ -15,-11 | -4,-3 ]',
'torus_bundle',
5.66644578172?,
'v2230',
'(0, 1)'],
['T x I / [ -18,-5 | -7,-2 ]',
'torus_bundle',
6.10565365397?,
'v2898',
'(1, 1)'],
['T x I / [ -19,-15 | -5,-4 ]',
'torus_bundle',
5.97824056586?,
't06263',
'(0, 1)'],
['T x I / [ -19,-8 | -7,-3 ]',
'torus_bundle',
6.37714255018?,
'v3247',
'(0, 1)'],
['T x I / [ -2,-1 | -1,-1 ]',
'torus_bundle',
2.0298832128193?,
'm003',
'(-1, 2)'],
['T x I / [ -21,-13 | -8,-5 ]',
'torus_bundle',
6.791984042028?,
'v3510',
'(0, 1)'],
['T x I / [ -25,-18 | -18,-13 ]',
'torus_bundle',
7.55501476820?,
't12547',
'(1, 0)'],
['T x I / [ -27,-10 | -8,-3 ]',
'torus_bundle',
6.951839008429?,
't10730',
'(1, 0)'],
['T x I / [ -29,-12 | -12,-5 ]',
'torus_bundle',
7.327724753418?,
't12051',
'(1, 0)'],
['T x I / [ -29,-18 | -8,-5 ]',
'torus_bundle',
7.18613966342?,
't11613',
'(0, 1)'],
['T x I / [ -3,-2 | -1,-1 ]',
'torus_bundle',
2.666744783449?,
'm010',
'(-2, 1)'],
['T x I / [ -30,-19 | -11,-7 ]',
'torus_bundle',
7.42259588346?,
't12294',
'(0, 1)'],
['T x I / [ -34,-13 | -13,-5 ]',
'torus_bundle',
7.64171059443?,
't12649',
'(1, 0)'],
['T x I / [ -34,-21 | -21,-13 ]',
'torus_bundle',
8.11953285128?,
't12838',
'(1, 0)'],
['T x I / [ -4,-3 | -1,-1 ]',
'torus_bundle',
2.989120282930?,
'm022',
'(2, 1)'],
['T x I / [ -41,-30 | -15,-11 ]',
'torus_bundle',
8.00023435035?,
'o9_39897',
'(0, 1)'],
['T x I / [ -49,-18 | -19,-7 ]',
'torus_bundle',
8.31910985858?,
'o9_42480',
'(1, 0)'],
['T x I / [ -5,-2 | -2,-1 ]',
'torus_bundle',
3.6638623767089?,
'm135',
'(-1, 1)'],
['T x I / [ -5,-3 | -3,-2 ]',
'torus_bundle',
4.059766425639?,
'm207',
'(-1, 1)'],
['T x I / [ -5,-4 | -1,-1 ]',
'torus_bundle',
3.177293278601?,
'm040',
'(-2, 1)'],
['T x I / [ -50,-21 | -19,-8 ]',
'torus_bundle',
8.44022021171?,
'o9_43230',
'(1, 0)'],
['T x I / [ -55,-34 | -21,-13 ]',
'torus_bundle',
8.82399715650?,
'o9_44145',
'(1, 0)'],
['T x I / [ -6,-5 | -1,-1 ]',
'torus_bundle',
3.296902414327?,
's001',
'(-2, 1)'],
['T x I / [ -7,-3 | -2,-1 ]',
'torus_bundle',
4.177751073190?,
'm234',
'(1, 1)'],
['T x I / [ -8,-5 | -3,-2 ]',
'torus_bundle',
4.75170196552?,
'm369',
'(-1, 1)'],
['T x I / [ -9,-4 | -2,-1 ]',
'torus_bundle',
4.464658911549?,
's299',
'(-1, 1)'],
['T x I / [ 10,3 | 3,1 ]', 'torus_bundle', 4.813819186104?, 's464', '(0, 1)'],
['T x I / [ 11,5 | 2,1 ]', 'torus_bundle', 4.63643309583?, 'v0650', '(1, 1)'],
['T x I / [ 11,7 | 3,2 ]',
'torus_bundle',
5.133548425107?,
's640',
'(-1, 1)'],
['T x I / [ 11,8 | 4,3 ]', 'torus_bundle', 5.333489566898?, 's787', '(0, 1)'],
['T x I / [ 13,4 | 3,1 ]', 'torus_bundle', 5.17067407823?, 'v1276', '(0, 1)'],
['T x I / [ 13,5 | 5,2 ]', 'torus_bundle', 5.62537824957?, 's892', '(0, 1)'],
['T x I / [ 13,8 | 8,5 ]', 'torus_bundle', 6.089649638458?, 's961', '(0, 1)'],
['T x I / [ 15,11 | 4,3 ]',
'torus_bundle',
5.66644578172?,
'v2231',
'(1, 1)'],
['T x I / [ 19,8 | 7,3 ]', 'torus_bundle', 6.37714255018?, 'v3246', '(0, 1)'],
['T x I / [ 2,1 | 1,1 ]', 'torus_bundle', 2.0298832128193?, 'm004', '(0, 1)'],
['T x I / [ 21,13 | 8,5 ]',
'torus_bundle',
6.791984042028?,
'v3511',
'(0, 1)'],
['T x I / [ 25,18 | 18,13 ]',
'torus_bundle',
7.55501476820?,
't12548',
'(1, 0)'],
['T x I / [ 29,12 | 12,5 ]',
'torus_bundle',
7.327724753418?,
't12050',
'(1, 0)'],
['T x I / [ 3,2 | 1,1 ]', 'torus_bundle', 2.666744783449?, 'm009', '(1, 1)'],
['T x I / [ 30,19 | 11,7 ]',
'torus_bundle',
7.422595883452?,
't12295',
'(1, 0)'],
['T x I / [ 34,13 | 13,5 ]',
'torus_bundle',
7.64171059443?,
't12648',
'(1, 0)'],
['T x I / [ 34,21 | 21,13 ]',
'torus_bundle',
8.11953285128?,
't12839',
'(1, 0)'],
['T x I / [ 37,10 | 11,3 ]',
'torus_bundle',
7.42631541712?,
'o9_32934',
'(0, 1)'],
['T x I / [ 4,3 | 1,1 ]', 'torus_bundle', 2.989120282930?, 'm023', '(-1, 1)'],
['T x I / [ 41,11 | 26,7 ]',
'torus_bundle',
7.782201805721?,
'o9_37557',
'(1, 0)'],
['T x I / [ 41,17 | 12,5 ]',
'torus_bundle',
7.853469097890?,
'o9_38403',
'(1, 0)'],
['T x I / [ 41,30 | 15,11 ]',
'torus_bundle',
8.00023435035?,
'o9_39894',
'(1, 0)'],
['T x I / [ 49,18 | 19,7 ]',
'torus_bundle',
8.31910985858?,
'o9_42479',
'(1, 0)'],
['T x I / [ 5,2 | 2,1 ]', 'torus_bundle', 3.663862376709?, 'm136', '(0, 1)'],
['T x I / [ 5,3 | 3,2 ]', 'torus_bundle', 4.059766425639?, 'm206', '(0, 1)'],
['T x I / [ 5,4 | 1,1 ]', 'torus_bundle', 3.177293278601?, 'm039', '(2, 1)'],
['T x I / [ 50,21 | 19,8 ]',
'torus_bundle',
8.44022021171?,
'o9_43229',
'(1, 0)'],
['T x I / [ 55,34 | 21,13 ]',
'torus_bundle',
8.82399715650?,
'o9_44144',
'(1, 0)'],
['T x I / [ 6,5 | 1,1 ]', 'torus_bundle', 3.296902414327?, 's000', '(2, 1)'],
['T x I / [ 7,3 | 2,1 ]', 'torus_bundle', 4.177751073190?, 'm235', '(0, 1)'],
['T x I / [ 7,6 | 1,1 ]', 'torus_bundle', 3.37759740824?, 'v0000', '(2, 1)'],
['T x I / [ 8,5 | 3,2 ]', 'torus_bundle', 4.751701965518?, 'm370', '(0, 1)'],
['T x I / [ 9,4 | 2,1 ]', 'torus_bundle', 4.46465891155?, 's298', '(1, 1)']]
We check which manifolds arise in more than one way.
for i in range(len(volt_new)-1):
x=volt_new[i]
y=volt_new[i+1]
if x[0]==y[0]:
print(x)
print(y)
print('------')
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's781', '(1, 0)']
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's786', '(1, 0)']
------
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2229', '(1, 0)']
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2230', '(1, 0)']
------
['L(4,1) # L(6,1)', 'connect_sum', 5.866445349336?, 't05624', '(1, 0)']
['L(4,1) # L(6,1)', 'connect_sum', 5.86644534934?, 't05625', '(1, 0)']
------
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035200?, 'o9_13333', '(1, 0)']
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035201?, 'o9_13334', '(1, 0)']
------
['L(4,1) # RP3', 'connect_sum', 3.6638623767089?, 'm135', '(0, 1)']
['L(4,1) # RP3', 'connect_sum', 3.6638623767089?, 'm135', '(1, 0)']
------
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3219', '(1, 0)']
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3221', '(1, 0)']
------
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3221', '(1, 0)']
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3228', '(1, 0)']
------
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09262', '(1, 0)']
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09263', '(1, 0)']
------
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23974', '(1, 0)']
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23976', '(1, 0)']
------
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12062', '(1, 0)']
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12063', '(1, 0)']
------
['SFS [S2: (2,1) (3,2) (3,-1)]', 'finite', 2.0298832128193?, 'm003', '(-2, 1)']
['SFS [S2: (2,1) (3,2) (3,-1)]', 'finite', 2.0298832128193?, 'm003', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]')])", 'graph', 7.78180863689?, 'o9_37549', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]')])", 'graph', 7.78180863689?, 'o9_37550', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 8.05755326323?, 'o9_40448', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 8.05755326323?, 'o9_40449', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 7.70691180281?, 'o9_36572', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 7.70691180281?, 'o9_36573', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (3,2)]')])", 'graph', 5.698441750940?, 'v2284', '(0, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (3,2)]')])", 'graph', 5.698441750940?, 'v2285', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (4,7)]')])", 'graph', 5.893627044281?, 't05802', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (4,7)]')])", 'graph', 5.893627044281?, 't05803', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (7,4)]')])", 'graph', 6.05870491502?, 'o9_14445', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (7,4)]')])", 'graph', 6.05870491502?, 'o9_14446', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (8,3)]')])", 'graph', 6.08503092554?, 'o9_14919', '(0, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (8,3)]')])", 'graph', 6.08503092554?, 'o9_14920', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (4,1)]')])", 'graph', 5.92036990476?, 't05975', '(-1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (4,1)]')])", 'graph', 5.920369904756?, 't05976', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (5,2)]')])", 'graph', 5.981919247764?, 't06291', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (5,2)]')])", 'graph', 5.981919247764?, 't06292', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (4,-3)]'), ('SFSpace', 'SFS [Or, g=0 + 3 punctures: (1,3)]')])", 'graph', 8.30510564923?, 'o9_42389', '(1, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (4,-3)]'), ('SFSpace', 'SFS [Or, g=0 + 3 punctures: (1,3)]')])", 'graph', 8.3051056492?, 'o9_42390', '(0, 1)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [A: (2,1)] U/n SFS [D: (2,1) (2,1)], m = [ 1,-2 | 0,-1 ], n = [ 1,2 | 1,1 ]', 'graph', 7.327724753418?, 't12045', '(1, 1)']
['SFS [D: (2,1) (2,1)] U/m SFS [A: (2,1)] U/n SFS [D: (2,1) (2,1)], m = [ 1,-2 | 0,-1 ], n = [ 1,2 | 1,1 ]', 'graph', 7.327724753418?, 't12045', '(-1, 1)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (2,1)], m = [ 1,2 | 0,-1 ]', 'graph', 6.35458655720?, 't07933', '(-1, 1)']
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (2,1)], m = [ 1,2 | 0,-1 ]', 'graph', 6.354586557201?, 't07939', '(1, 1)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.0298832128193?, 'm004', '(-4, 1)']
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.0298832128193?, 'm004', '(4, 1)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.0298832128193?, 'm003', '(1, 2)']
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.0298832128193?, 'm003', '(-3, 2)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,1)], m = [ -1,2 | 0,1 ]', 'graph', 3.663862376709?, 'm136', '(2, 1)']
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,1)], m = [ -1,2 | 0,1 ]', 'graph', 3.663862376709?, 'm136', '(-2, 1)']
------
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,2 | 0,1 ]', 'graph', 4.059766425639?, 'm206', '(-2, 1)']
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,2 | 0,1 ]', 'graph', 4.059766425639?, 'm206', '(2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm003')])", 'hyperbolic_piece', 6.345579305182?, 'v3198', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm003')])", 'hyperbolic_piece', 6.345579305182?, 'v3199', '(1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm004')])", 'hyperbolic_piece', 5.579312783682?, 'v2050', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm004')])", 'hyperbolic_piece', 5.579312783682?, 'v2051', '(-2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm007')])", 'hyperbolic_piece', 6.090054170794?, 'v2876', '(2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm007')])", 'hyperbolic_piece', 6.09005417080?, 'v2877', '(-2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm009')])", 'hyperbolic_piece', 6.270718240014?, 't07592', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm009')])", 'hyperbolic_piece', 6.27071824002?, 't07593', '(2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42486', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42487', '(1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42487', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42489', '(-1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.61241520146?, 'o9_43799', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.61241520146?, 'o9_43800', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm015')])", 'hyperbolic_piece', 6.54077849855?, 't08823', '(-2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm015')])", 'hyperbolic_piece', 6.54077849855?, 't08824', '(2, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm036')])", 'hyperbolic_piece', 6.99718914780?, 't10931', '(2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm036')])", 'hyperbolic_piece', 6.99718914780?, 't10932', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.00023435035?, 'o9_39899', '(-2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.000234350347?, 'o9_39902', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm207')])", 'hyperbolic_piece', 8.77865880318?, 'o9_44075', '(-1, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm207')])", 'hyperbolic_piece', 8.77865880318?, 'o9_44076', '(0, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34171', '(1, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34172', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34172', '(-2, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34173', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34173', '(-2, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34174', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm129')])", 'hyperbolic_piece', 7.90060972026?, 'o9_38894', '(-1, 1)']
["JSJ([('hyperbolic', 'm129')])", 'hyperbolic_piece', 7.90060972026?, 'o9_38895', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39337', '(-1, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39338', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39338', '(2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39339', '(-1, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39339', '(-1, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924779?, 'o9_39340', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924779?, 'o9_39340', '(-2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39341', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39341', '(2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39342', '(-2, 1)']
------
['SFS [D: (2,1) (2,1)] U m003 (Z_20)', 'hyperbolic_piece', 5.91674573519?, 'v2642', '(1, 1)']
['SFS [D: (2,1) (2,1)] U m003 (Z_20)', 'hyperbolic_piece', 5.916745735183?, 'v2643', '(-2, 1)']
------
['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(-1, 1)']
['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(0, 1)']
------
['SFS [S2: (2,1) (3,1) (7,-6)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-1, 1)']
['SFS [S2: (2,1) (3,1) (7,-6)]', 'seifert_ator', 2.0298832128193?, 'm004', '(1, 1)']
------
['SFS [S2: (2,1) (4,1) (4,-1)]', 'seifert_ator', 3.177293278601?, 'm037', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,-1)]', 'seifert_ator', 3.177293278601?, 'm040', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,11)]', 'seifert_ator', 3.651324930474?, 't00226', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,11)]', 'seifert_ator', 3.65132493048?, 'o9_00160', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,3)]', 'seifert_ator', 3.596882244932?, 's056', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,3)]', 'seifert_ator', 3.596882244932?, 'v0030', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,7)]', 'seifert_ator', 3.639386687137?, 'v0130', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,7)]', 'seifert_ator', 3.63938668714?, 't00090', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (5,-4)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-2, 1)']
['SFS [S2: (2,1) (4,1) (5,-4)]', 'seifert_ator', 2.0298832128193?, 'm004', '(2, 1)']
------
['SFS [S2: (3,1) (3,1) (4,-3)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-3, 1)']
['SFS [S2: (3,1) (3,1) (4,-3)]', 'seifert_ator', 2.0298832128193?, 'm004', '(3, 1)']
------
Some of these are because the manifold has some symmetry like the figure 8, m004, and thus have two surgeries yielding the same manifold. But some others are more interesting. We print the interesting ones.
for i in range(len(volt_new)-1):
x=volt_new[i]
y=volt_new[i+1]
if x[0]==y[0]:
if x[3]!=y[3]:
print(x)
print(y)
print('------')
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's781', '(1, 0)']
['L(4,1) # L(4,1)', 'connect_sum', 5.333489566898?, 's786', '(1, 0)']
------
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2229', '(1, 0)']
['L(4,1) # L(5,1)', 'connect_sum', 5.66644578172?, 'v2230', '(1, 0)']
------
['L(4,1) # L(6,1)', 'connect_sum', 5.866445349336?, 't05624', '(1, 0)']
['L(4,1) # L(6,1)', 'connect_sum', 5.86644534934?, 't05625', '(1, 0)']
------
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035200?, 'o9_13333', '(1, 0)']
['L(4,1) # L(7,1)', 'connect_sum', 5.99291035201?, 'o9_13334', '(1, 0)']
------
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3219', '(1, 0)']
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3221', '(1, 0)']
------
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3221', '(1, 0)']
['L(4,1) # S2 x S1', 'connect_sum', 6.35458655720?, 'v3228', '(1, 0)']
------
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09262', '(1, 0)']
['L(5,1) # S2 x S1', 'connect_sum', 6.64720315893?, 't09263', '(1, 0)']
------
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23974', '(1, 0)']
['L(6,1) # S2 x S1', 'connect_sum', 6.83177049648?, 'o9_23976', '(1, 0)']
------
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12062', '(1, 0)']
['S2 x S1 # S2 x S1', 'connect_sum', 7.327724753418?, 't12063', '(1, 0)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]')])", 'graph', 7.78180863689?, 'o9_37549', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]')])", 'graph', 7.78180863689?, 'o9_37550', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 8.05755326323?, 'o9_40448', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 8.05755326323?, 'o9_40449', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 7.70691180281?, 'o9_36572', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (2,3)]')])", 'graph', 7.70691180281?, 'o9_36573', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (3,2)]')])", 'graph', 5.698441750940?, 'v2284', '(0, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (3,2)]')])", 'graph', 5.698441750940?, 'v2285', '(-1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (4,7)]')])", 'graph', 5.893627044281?, 't05802', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (4,7)]')])", 'graph', 5.893627044281?, 't05803', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (7,4)]')])", 'graph', 6.05870491502?, 'o9_14445', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (7,4)]')])", 'graph', 6.05870491502?, 'o9_14446', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (8,3)]')])", 'graph', 6.08503092554?, 'o9_14919', '(0, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,1)]'), ('SFSpace', 'SFS [A: (8,3)]')])", 'graph', 6.08503092554?, 'o9_14920', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (4,1)]')])", 'graph', 5.92036990476?, 't05975', '(-1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (4,1)]')])", 'graph', 5.920369904756?, 't05976', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (5,2)]')])", 'graph', 5.981919247764?, 't06291', '(1, 1)']
["JSJ([('SFSpace', 'SFS [A: (2,3)]'), ('SFSpace', 'SFS [A: (5,2)]')])", 'graph', 5.981919247764?, 't06292', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (4,-3)]'), ('SFSpace', 'SFS [Or, g=0 + 3 punctures: (1,3)]')])", 'graph', 8.30510564923?, 'o9_42389', '(1, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (4,-3)]'), ('SFSpace', 'SFS [Or, g=0 + 3 punctures: (1,3)]')])", 'graph', 8.3051056492?, 'o9_42390', '(0, 1)']
------
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (2,1)], m = [ 1,2 | 0,-1 ]', 'graph', 6.35458655720?, 't07933', '(-1, 1)']
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (2,1)], m = [ 1,2 | 0,-1 ]', 'graph', 6.354586557201?, 't07939', '(1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm003')])", 'hyperbolic_piece', 6.345579305182?, 'v3198', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm003')])", 'hyperbolic_piece', 6.345579305182?, 'v3199', '(1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm004')])", 'hyperbolic_piece', 5.579312783682?, 'v2050', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm004')])", 'hyperbolic_piece', 5.579312783682?, 'v2051', '(-2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm007')])", 'hyperbolic_piece', 6.090054170794?, 'v2876', '(2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm007')])", 'hyperbolic_piece', 6.09005417080?, 'v2877', '(-2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm009')])", 'hyperbolic_piece', 6.270718240014?, 't07592', '(-2, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm009')])", 'hyperbolic_piece', 6.27071824002?, 't07593', '(2, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42486', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42487', '(1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42487', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm130')])", 'hyperbolic_piece', 8.31975161233?, 'o9_42489', '(-1, 1)']
------
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.61241520146?, 'o9_43799', '(1, 1)']
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.61241520146?, 'o9_43800', '(0, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm015')])", 'hyperbolic_piece', 6.54077849855?, 't08823', '(-2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm015')])", 'hyperbolic_piece', 6.54077849855?, 't08824', '(2, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm036')])", 'hyperbolic_piece', 6.99718914780?, 't10931', '(2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm036')])", 'hyperbolic_piece', 6.99718914780?, 't10932', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.00023435035?, 'o9_39899', '(-2, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm135')])", 'hyperbolic_piece', 8.000234350347?, 'o9_39902', '(1, 1)']
------
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm207')])", 'hyperbolic_piece', 8.77865880318?, 'o9_44075', '(-1, 1)']
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm207')])", 'hyperbolic_piece', 8.77865880318?, 'o9_44076', '(0, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34171', '(1, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34172', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34172', '(-2, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34173', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34173', '(-2, 1)']
["JSJ([('hyperbolic', 'm125')])", 'hyperbolic_piece', 7.51768989648?, 'o9_34174', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm129')])", 'hyperbolic_piece', 7.90060972026?, 'o9_38894', '(-1, 1)']
["JSJ([('hyperbolic', 'm129')])", 'hyperbolic_piece', 7.90060972026?, 'o9_38895', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39337', '(-1, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39338', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39338', '(2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39339', '(-1, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39339', '(-1, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924779?, 'o9_39340', '(-2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924779?, 'o9_39340', '(-2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39341', '(2, 1)']
------
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39341', '(2, 1)']
["JSJ([('hyperbolic', 'm202')])", 'hyperbolic_piece', 7.94057924778?, 'o9_39342', '(-2, 1)']
------
['SFS [D: (2,1) (2,1)] U m003 (Z_20)', 'hyperbolic_piece', 5.91674573519?, 'v2642', '(1, 1)']
['SFS [D: (2,1) (2,1)] U m003 (Z_20)', 'hyperbolic_piece', 5.916745735183?, 'v2643', '(-2, 1)']
------
['SFS [S2: (2,1) (4,1) (4,-1)]', 'seifert_ator', 3.177293278601?, 'm037', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,-1)]', 'seifert_ator', 3.177293278601?, 'm040', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,11)]', 'seifert_ator', 3.651324930474?, 't00226', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,11)]', 'seifert_ator', 3.65132493048?, 'o9_00160', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,3)]', 'seifert_ator', 3.596882244932?, 's056', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,3)]', 'seifert_ator', 3.596882244932?, 'v0030', '(0, 1)']
------
['SFS [S2: (2,1) (4,1) (4,7)]', 'seifert_ator', 3.639386687137?, 'v0130', '(0, 1)']
['SFS [S2: (2,1) (4,1) (4,7)]', 'seifert_ator', 3.63938668714?, 't00090', '(0, 1)']
------
Here we see several potential infinite families.
TO DO: Work those out.
# We save the list as pickel file
import pickle
with open('volt_sorted_by_type.pickle', 'wb') as f:
pickle.dump(volt_new, f)
Next, we sort the list by volumes.
volt_new.sort(key=lambda x: (x[2],x[3],x[1],x[2]))
volt_new
[['S3', 'S3', 2.0298832128193?, 'm004', '(1, 0)'],
['SFS [S2: (2,1) (3,2) (3,-1)]',
'finite',
2.0298832128193?,
'm003',
'(-2, 1)'],
['SFS [S2: (2,1) (3,2) (3,-1)]',
'finite',
2.0298832128193?,
'm003',
'(1, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]',
'graph',
2.0298832128193?,
'm004',
'(-4, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]',
'graph',
2.0298832128193?,
'm004',
'(4, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]',
'graph',
2.0298832128193?,
'm003',
'(1, 2)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]',
'graph',
2.0298832128193?,
'm003',
'(-3, 2)'],
['L(10,3)', 'lens_space', 2.0298832128193?, 'm003', '(1, 0)'],
['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(-1, 1)'],
['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(0, 1)'],
['SFS [S2: (2,1) (3,1) (7,-6)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(-1, 1)'],
['SFS [S2: (2,1) (3,1) (7,-6)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(1, 1)'],
['SFS [S2: (2,1) (4,1) (5,-4)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(-2, 1)'],
['SFS [S2: (2,1) (4,1) (5,-4)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(2, 1)'],
['SFS [S2: (3,1) (3,1) (4,-3)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(-3, 1)'],
['SFS [S2: (3,1) (3,1) (4,-3)]',
'seifert_ator',
2.0298832128193?,
'm004',
'(3, 1)'],
['T x I / [ -2,-1 | -1,-1 ]',
'torus_bundle',
2.0298832128193?,
'm003',
'(-1, 2)'],
['T x I / [ 2,1 | 1,1 ]', 'torus_bundle', 2.0298832128193?, 'm004', '(0, 1)'],
['SFS [S2: (2,1) (2,1) (3,2)]', 'finite', 2.5689706009367?, 'm006', '(1, 1)'],
['SFS [S2: (2,1) (2,1) (5,-2)]',
'finite',
2.5689706009367?,
'm007',
'(1, 1)'],
['SFS [S2: (2,1) (3,2) (4,-3)]',
'finite',
2.5689706009367?,
'm006',
'(-1, 1)'],
['SFS [A: (2,1)] / [ 0,-1 | -1,0 ]',
'graph',
2.5689706009367?,
'm006',
'(-3, 1)'],
['SFS [A: (2,1)] / [ 0,1 | 1,0 ]',
'graph',
2.5689706009367?,
'm007',
'(-3, 1)'],
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,1 | 0,1 ]',
'graph',
2.5689706009367?,
'm006',
'(1, 2)'],
['L(15,4)', 'lens_space', 2.5689706009367?, 'm006', '(0, 1)'],
['L(3,1)', 'lens_space', 2.5689706009367?, 'm007', '(1, 0)'],
['L(5,2)', 'lens_space', 2.5689706009367?, 'm006', '(1, 0)'],
['SFS [S2: (2,1) (3,1) (7,-5)]',
'seifert_ator',
2.5689706009367?,
'm006',
'(-2, 1)'],
['SFS [S2: (2,1) (3,1) (9,-7)]',
'seifert_ator',
2.5689706009367?,
'm007',
'(-2, 1)'],
['SFS [S2: (2,1) (4,1) (5,-3)]',
'seifert_ator',
2.5689706009367?,
'm007',
'(-1, 1)'],
['SFS [S2: (3,1) (3,1) (3,-1)]',
'seifert_ator',
2.5689706009367?,
'm007',
'(0, 1)'],
['L(3,1) # RP3', 'connect_sum', 2.666744783449?, 'm010', '(-1, 1)'],
['SFS [S2: (2,1) (2,1) (4,-1)]', 'finite', 2.666744783449?, 'm010', '(0, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,2 | 0,1 ]',
'graph',
2.666744783449?,
'm009',
'(3, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,1)], m = [ 0,1 | 1,0 ]',
'graph',
2.666744783449?,
'm009',
'(-3, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,3)], m = [ 0,1 | 1,1 ]',
'graph',
2.666744783449?,
'm010',
'(2, 1)'],
['L(6,1)', 'lens_space', 2.666744783449?, 'm010', '(1, 0)'],
['RP3', 'lens_space', 2.666744783449?, 'm009', '(1, 0)'],
['SFS [S2: (2,1) (3,1) (8,-7)]',
'seifert_ator',
2.666744783449?,
'm009',
'(0, 1)'],
['SFS [S2: (2,1) (4,1) (6,-5)]',
'seifert_ator',
2.666744783449?,
'm009',
'(-1, 1)'],
['SFS [S2: (3,1) (3,1) (5,-4)]',
'seifert_ator',
2.666744783449?,
'm009',
'(-2, 1)'],
['SFS [S2: (3,1) (3,2) (3,-1)]',
'seifert_ator',
2.666744783449?,
'm010',
'(1, 1)'],
['T x I / [ -3,-2 | -1,-1 ]',
'torus_bundle',
2.666744783449?,
'm010',
'(-2, 1)'],
['T x I / [ 3,2 | 1,1 ]', 'torus_bundle', 2.666744783449?, 'm009', '(1, 1)'],
['SFS [S2: (2,1) (2,1) (3,-2)]',
'finite',
2.7818339123961?,
'm011',
'(1, 1)'],
['SFS [S2: (2,1) (3,2) (4,-1)]',
'finite',
2.7818339123961?,
'm011',
'(-1, 1)'],
['SFS [S2: (2,1) (3,2) (5,-3)]',
'finite',
2.7818339123961?,
'm011',
'(2, 1)'],
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]',
'graph',
2.7818339123961?,
'm011',
'(-1, 2)'],
['L(13,3)', 'lens_space', 2.7818339123961?, 'm011', '(1, 0)'],
['L(9,2)', 'lens_space', 2.7818339123961?, 'm011', '(0, 1)'],
['SFS [S2: (2,1) (3,1) (5,-3)]',
'finite',
2.8281220883308?,
'm017',
'(1, 1)'],
['SFS [A: (2,1)] / [ 0,-1 | -1,1 ]',
'graph',
2.8281220883308?,
'm017',
'(2, 1)'],
['SFS [A: (2,1)] / [ 0,1 | 1,-1 ]',
'graph',
2.8281220883308?,
'm015',
'(-2, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,1 ]',
'graph',
2.8281220883308?,
'm017',
'(-2, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 1,1 | 0,1 ]',
'graph',
2.8281220883308?,
'm016',
'(2, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,0 ]',
'graph',
2.8281220883308?,
'm015',
'(2, 1)'],
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,2)], m = [ -1,1 | 0,1 ]',
'graph',
2.8281220883308?,
'm016',
'(-1, 2)'],
['L(14,3)', 'lens_space', 2.8281220883308?, 'm017', '(0, 1)'],
['L(18,5)', 'lens_space', 2.8281220883308?, 'm016', '(0, 1)'],
['L(19,7)', 'lens_space', 2.8281220883308?, 'm016', '(-1, 1)'],
['L(21,8)', 'lens_space', 2.8281220883308?, 'm017', '(-1, 1)'],
['L(7,2)', 'lens_space', 2.8281220883308?, 'm017', '(1, 0)'],
['SFS [S2: (2,1) (3,1) (11,-9)]',
'seifert_ator',
2.8281220883308?,
'm015',
'(-1, 1)'],
['SFS [S2: (2,1) (4,1) (7,-5)]',
'seifert_ator',
2.8281220883308?,
'm015',
'(0, 1)'],
['SFS [S2: (3,1) (3,1) (5,-3)]',
'seifert_ator',
2.8281220883308?,
'm015',
'(1, 1)'],
['SFS [S2: (2,1) (3,2) (5,-2)]',
'finite',
2.9441064866767?,
'm019',
'(-1, 1)'],
['SFS [D: (2,1) (3,2)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]',
'graph',
2.9441064866767?,
'm019',
'(-2, 1)'],
['L(11,3)', 'lens_space', 2.9441064866767?, 'm019', '(1, 1)'],
['L(17,5)', 'lens_space', 2.9441064866767?, 'm019', '(0, 1)'],
['SFS [S2: (2,1) (3,1) (4,-1)]', 'finite', 2.989120282930?, 'm022', '(0, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,1)], m = [ 0,1 | 1,0 ]',
'graph',
2.989120282930?,
'm023',
'(3, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,4)], m = [ 0,1 | 1,1 ]',
'graph',
2.989120282930?,
'm022',
'(-2, 1)'],
['L(7,1)', 'lens_space', 2.989120282930?, 'm022', '(1, 0)'],
['SFS [S2: (2,1) (3,1) (9,-8)]',
'seifert_ator',
2.989120282930?,
'm023',
'(0, 1)'],
['SFS [S2: (2,1) (4,1) (7,-6)]',
'seifert_ator',
2.989120282930?,
'm023',
'(1, 1)'],
['SFS [S2: (3,1) (3,1) (6,-5)]',
'seifert_ator',
2.989120282930?,
'm023',
'(2, 1)'],
['SFS [S2: (3,2) (3,2) (4,-3)]',
'seifert_ator',
2.989120282930?,
'm022',
'(-1, 1)'],
['T x I / [ -4,-3 | -1,-1 ]',
'torus_bundle',
2.989120282930?,
'm022',
'(2, 1)'],
['T x I / [ 4,3 | 1,1 ]', 'torus_bundle', 2.989120282930?, 'm023', '(-1, 1)'],
['SFS [S2: (2,1) (3,1) (3,2)]', 'finite', 3.0593380577790?, 'm026', '(1, 1)'],
['SFS [S2: (2,1) (3,2) (5,-4)]',
'finite',
3.0593380577790?,
'm026',
'(-1, 1)'],
['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (4,1)], m = [ -1,1 | 0,1 ]',
'graph',
3.0593380577790?,
'm026',
'(1, 2)'],
['L(19,4)', 'lens_space', 3.0593380577790?, 'm026', '(0, 1)'],
['L(8,3)', 'lens_space', 3.0593380577790?, 'm026', '(1, 0)'],
['SFS [S2: (2,1) (3,1) (3,-2)]', 'finite', 3.121334773013?, 'm027', '(1, 1)'],
['SFS [S2: (2,1) (3,2) (5,-1)]',
'finite',
3.121334773013?,
'm027',
'(-1, 1)'],
['SFS [D: (2,1) (3,2)] U/m SFS [D: (2,1) (4,1)], m = [ -1,1 | 1,0 ]',
'graph',
3.121334773013?,
'm027',
'(-1, 2)'],
['L(16,3)', 'lens_space', 3.121334773013?, 'm027', '(1, 0)'],
['SFS [S2: (2,1) (3,2) (7,-5)]',
'seifert_ator',
3.121334773013?,
'm027',
'(2, 1)'],
['SFS [S2: (2,1) (2,1) (5,2)]', 'finite', 3.148509826441?, 'm030', '(2, 1)'],
['SFS [S2: (2,1) (2,1) (7,-2)]',
'finite',
3.148509826441?,
'm029',
'(-1, 1)'],
['SFS [S2: (2,1) (3,1) (3,1)]', 'finite', 3.148509826441?, 'm030', '(1, 1)'],
['SFS [A: (3,1)] / [ 0,-1 | -1,0 ]',
'graph',
3.148509826441?,
'm030',
'(-2, 1)'],
['SFS [A: (3,1)] / [ 0,1 | 1,0 ]',
'graph',
3.148509826441?,
'm029',
'(3, 1)'],
['SFS [S2: (2,1) (3,1) (11,-8)]',
'seifert_ator',
3.148509826441?,
'm030',
'(-1, 1)'],
['SFS [S2: (2,1) (3,1) (13,-10)]',
'seifert_ator',
3.148509826441?,
'm029',
'(2, 1)'],
['SFS [S2: (2,1) (4,1) (5,-2)]',
'seifert_ator',
3.148509826441?,
'm030',
'(0, 1)'],
['SFS [S2: (2,1) (4,1) (7,-4)]',
'seifert_ator',
3.148509826441?,
'm029',
'(1, 1)'],
['SFS [S2: (3,1) (3,1) (4,-1)]',
'seifert_ator',
3.148509826441?,
'm029',
'(0, 1)'],
['SFS [S2: (2,1) (3,1) (3,-1)]',
'finite',
3.163963228884?,
'm033',
'(-1, 1)'],
['SFS [A: (2,1)] / [ 0,-1 | -1,2 ]',
'graph',
3.163963228884?,
'm033',
'(-2, 1)'],
['SFS [A: (2,1)] / [ 0,1 | 1,-2 ]',
'graph',
3.163963228884?,
'm032',
'(2, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,2)], m = [ 0,1 | 1,0 ]',
'graph',
3.163963228884?,
'm032',
'(-2, 1)'],
['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,3)], m = [ 0,1 | 1,1 ]',
'graph',
3.163963228884?,
'm033',
'(2, 1)'],
['SFS [S2: (2,1) (3,1) (13,-11)]',
'seifert_ator',
3.163963228884?,
'm032',
'(1, 1)'],
['SFS [S2: (2,1) (4,1) (9,-7)]',
'seifert_ator',
3.163963228884?,
'm032',
'(0, 1)'],
['SFS [S2: (3,1) (3,1) (7,-5)]',
'seifert_ator',
3.163963228884?,
'm032',
'(-1, 1)'],
['SFS [S2: (3,2) (3,2) (3,-1)]',
'seifert_ator',
3.163963228884?,
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'o9_44080',
'(0, 1)'],
['T x I / [ -55,-34 | -21,-13 ]',
'torus_bundle',
8.82399715650?,
'o9_44145',
'(1, 0)'],
['T x I / [ 55,34 | 21,13 ]',
'torus_bundle',
8.82399715650?,
'o9_44144',
'(1, 0)'],
["JSJ([('SFSpace', 'M/n2 x~ S1'), ('hyperbolic', 'm206')])",
'hyperbolic_piece',
8.89600325562?,
'o9_44189',
'(1, 1)'],
["JSJ([('SFSpace', 'SFS [D: (2,1) (2,-1)]'), ('hyperbolic', 'm206')])",
'hyperbolic_piece',
8.89600325562?,
'o9_44190',
'(-1, 1)']]
# We save the list as pickel file
with open('volt_sorted_by_volume.pickle', 'wb') as f:
pickle.dump(volt_new, f)
The following list contains the 14 smallest (i.e with smallest volume) one cusped hyperbolic manifolds. If a non-hyperbolic manifold arises by surgery one one of these, we can compute its topological volume. We do this next.
small=['m003','m004','m006','m007','m009','m010','m011','m015','m016','m017','m019', 'm022', 'm023', 'm026']
volt_rigor=[]
for x in volt_new:
if x[3] in small:
volt_rigor.append(x)
len(volt_rigor)
84
volt_rigor
[['S3', 'S3', 2.0298832128193?, 'm004', '(1, 0)'], ['SFS [S2: (2,1) (3,2) (3,-1)]', 'finite', 2.0298832128193?, 'm003', '(-2, 1)'], ['SFS [S2: (2,1) (3,2) (3,-1)]', 'finite', 2.0298832128193?, 'm003', '(1, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.0298832128193?, 'm004', '(-4, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.0298832128193?, 'm004', '(4, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.0298832128193?, 'm003', '(1, 2)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.0298832128193?, 'm003', '(-3, 2)'], ['L(10,3)', 'lens_space', 2.0298832128193?, 'm003', '(1, 0)'], ['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(-1, 1)'], ['L(5,1)', 'lens_space', 2.0298832128193?, 'm003', '(0, 1)'], ['SFS [S2: (2,1) (3,1) (7,-6)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-1, 1)'], ['SFS [S2: (2,1) (3,1) (7,-6)]', 'seifert_ator', 2.0298832128193?, 'm004', '(1, 1)'], ['SFS [S2: (2,1) (4,1) (5,-4)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-2, 1)'], ['SFS [S2: (2,1) (4,1) (5,-4)]', 'seifert_ator', 2.0298832128193?, 'm004', '(2, 1)'], ['SFS [S2: (3,1) (3,1) (4,-3)]', 'seifert_ator', 2.0298832128193?, 'm004', '(-3, 1)'], ['SFS [S2: (3,1) (3,1) (4,-3)]', 'seifert_ator', 2.0298832128193?, 'm004', '(3, 1)'], ['T x I / [ -2,-1 | -1,-1 ]', 'torus_bundle', 2.0298832128193?, 'm003', '(-1, 2)'], ['T x I / [ 2,1 | 1,1 ]', 'torus_bundle', 2.0298832128193?, 'm004', '(0, 1)'], ['SFS [S2: (2,1) (2,1) (3,2)]', 'finite', 2.5689706009367?, 'm006', '(1, 1)'], ['SFS [S2: (2,1) (2,1) (5,-2)]', 'finite', 2.5689706009367?, 'm007', '(1, 1)'], ['SFS [S2: (2,1) (3,2) (4,-3)]', 'finite', 2.5689706009367?, 'm006', '(-1, 1)'], ['SFS [A: (2,1)] / [ 0,-1 | -1,0 ]', 'graph', 2.5689706009367?, 'm006', '(-3, 1)'], ['SFS [A: (2,1)] / [ 0,1 | 1,0 ]', 'graph', 2.5689706009367?, 'm007', '(-3, 1)'], ['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,1 | 0,1 ]', 'graph', 2.5689706009367?, 'm006', '(1, 2)'], ['L(15,4)', 'lens_space', 2.5689706009367?, 'm006', '(0, 1)'], ['L(3,1)', 'lens_space', 2.5689706009367?, 'm007', '(1, 0)'], ['L(5,2)', 'lens_space', 2.5689706009367?, 'm006', '(1, 0)'], ['SFS [S2: (2,1) (3,1) (7,-5)]', 'seifert_ator', 2.5689706009367?, 'm006', '(-2, 1)'], ['SFS [S2: (2,1) (3,1) (9,-7)]', 'seifert_ator', 2.5689706009367?, 'm007', '(-2, 1)'], ['SFS [S2: (2,1) (4,1) (5,-3)]', 'seifert_ator', 2.5689706009367?, 'm007', '(-1, 1)'], ['SFS [S2: (3,1) (3,1) (3,-1)]', 'seifert_ator', 2.5689706009367?, 'm007', '(0, 1)'], ['L(3,1) # RP3', 'connect_sum', 2.666744783449?, 'm010', '(-1, 1)'], ['SFS [S2: (2,1) (2,1) (4,-1)]', 'finite', 2.666744783449?, 'm010', '(0, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ -1,2 | 0,1 ]', 'graph', 2.666744783449?, 'm009', '(3, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.666744783449?, 'm009', '(-3, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (4,3)], m = [ 0,1 | 1,1 ]', 'graph', 2.666744783449?, 'm010', '(2, 1)'], ['L(6,1)', 'lens_space', 2.666744783449?, 'm010', '(1, 0)'], ['RP3', 'lens_space', 2.666744783449?, 'm009', '(1, 0)'], ['SFS [S2: (2,1) (3,1) (8,-7)]', 'seifert_ator', 2.666744783449?, 'm009', '(0, 1)'], ['SFS [S2: (2,1) (4,1) (6,-5)]', 'seifert_ator', 2.666744783449?, 'm009', '(-1, 1)'], ['SFS [S2: (3,1) (3,1) (5,-4)]', 'seifert_ator', 2.666744783449?, 'm009', '(-2, 1)'], ['SFS [S2: (3,1) (3,2) (3,-1)]', 'seifert_ator', 2.666744783449?, 'm010', '(1, 1)'], ['T x I / [ -3,-2 | -1,-1 ]', 'torus_bundle', 2.666744783449?, 'm010', '(-2, 1)'], ['T x I / [ 3,2 | 1,1 ]', 'torus_bundle', 2.666744783449?, 'm009', '(1, 1)'], ['SFS [S2: (2,1) (2,1) (3,-2)]', 'finite', 2.7818339123961?, 'm011', '(1, 1)'], ['SFS [S2: (2,1) (3,2) (4,-1)]', 'finite', 2.7818339123961?, 'm011', '(-1, 1)'], ['SFS [S2: (2,1) (3,2) (5,-3)]', 'finite', 2.7818339123961?, 'm011', '(2, 1)'], ['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.7818339123961?, 'm011', '(-1, 2)'], ['L(13,3)', 'lens_space', 2.7818339123961?, 'm011', '(1, 0)'], ['L(9,2)', 'lens_space', 2.7818339123961?, 'm011', '(0, 1)'], ['SFS [S2: (2,1) (3,1) (5,-3)]', 'finite', 2.8281220883308?, 'm017', '(1, 1)'], ['SFS [A: (2,1)] / [ 0,-1 | -1,1 ]', 'graph', 2.8281220883308?, 'm017', '(2, 1)'], ['SFS [A: (2,1)] / [ 0,1 | 1,-1 ]', 'graph', 2.8281220883308?, 'm015', '(-2, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 0,1 | 1,1 ]', 'graph', 2.8281220883308?, 'm017', '(-2, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,1)], m = [ 1,1 | 0,1 ]', 'graph', 2.8281220883308?, 'm016', '(2, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,0 ]', 'graph', 2.8281220883308?, 'm015', '(2, 1)'], ['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (3,2)], m = [ -1,1 | 0,1 ]', 'graph', 2.8281220883308?, 'm016', '(-1, 2)'], ['L(14,3)', 'lens_space', 2.8281220883308?, 'm017', '(0, 1)'], ['L(18,5)', 'lens_space', 2.8281220883308?, 'm016', '(0, 1)'], ['L(19,7)', 'lens_space', 2.8281220883308?, 'm016', '(-1, 1)'], ['L(21,8)', 'lens_space', 2.8281220883308?, 'm017', '(-1, 1)'], ['L(7,2)', 'lens_space', 2.8281220883308?, 'm017', '(1, 0)'], ['SFS [S2: (2,1) (3,1) (11,-9)]', 'seifert_ator', 2.8281220883308?, 'm015', '(-1, 1)'], ['SFS [S2: (2,1) (4,1) (7,-5)]', 'seifert_ator', 2.8281220883308?, 'm015', '(0, 1)'], ['SFS [S2: (3,1) (3,1) (5,-3)]', 'seifert_ator', 2.8281220883308?, 'm015', '(1, 1)'], ['SFS [S2: (2,1) (3,2) (5,-2)]', 'finite', 2.9441064866767?, 'm019', '(-1, 1)'], ['SFS [D: (2,1) (3,2)] U/m SFS [D: (2,1) (3,2)], m = [ 0,1 | 1,1 ]', 'graph', 2.9441064866767?, 'm019', '(-2, 1)'], ['L(11,3)', 'lens_space', 2.9441064866767?, 'm019', '(1, 1)'], ['L(17,5)', 'lens_space', 2.9441064866767?, 'm019', '(0, 1)'], ['SFS [S2: (2,1) (3,1) (4,-1)]', 'finite', 2.989120282930?, 'm022', '(0, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,1)], m = [ 0,1 | 1,0 ]', 'graph', 2.989120282930?, 'm023', '(3, 1)'], ['SFS [D: (2,1) (2,1)] U/m SFS [D: (2,1) (5,4)], m = [ 0,1 | 1,1 ]', 'graph', 2.989120282930?, 'm022', '(-2, 1)'], ['L(7,1)', 'lens_space', 2.989120282930?, 'm022', '(1, 0)'], ['SFS [S2: (2,1) (3,1) (9,-8)]', 'seifert_ator', 2.989120282930?, 'm023', '(0, 1)'], ['SFS [S2: (2,1) (4,1) (7,-6)]', 'seifert_ator', 2.989120282930?, 'm023', '(1, 1)'], ['SFS [S2: (3,1) (3,1) (6,-5)]', 'seifert_ator', 2.989120282930?, 'm023', '(2, 1)'], ['SFS [S2: (3,2) (3,2) (4,-3)]', 'seifert_ator', 2.989120282930?, 'm022', '(-1, 1)'], ['T x I / [ -4,-3 | -1,-1 ]', 'torus_bundle', 2.989120282930?, 'm022', '(2, 1)'], ['T x I / [ 4,3 | 1,1 ]', 'torus_bundle', 2.989120282930?, 'm023', '(-1, 1)'], ['SFS [S2: (2,1) (3,1) (3,2)]', 'finite', 3.0593380577790?, 'm026', '(1, 1)'], ['SFS [S2: (2,1) (3,2) (5,-4)]', 'finite', 3.0593380577790?, 'm026', '(-1, 1)'], ['SFS [D: (2,1) (3,1)] U/m SFS [D: (2,1) (4,1)], m = [ -1,1 | 0,1 ]', 'graph', 3.0593380577790?, 'm026', '(1, 2)'], ['L(19,4)', 'lens_space', 3.0593380577790?, 'm026', '(0, 1)'], ['L(8,3)', 'lens_space', 3.0593380577790?, 'm026', '(1, 0)']]