Please, register with Moodle for this class.

Literatur: 1. R.H.Crowell and R.H. Fox: Introduction to Knot Theory, Springer 1963  (electronically available in library - you have to use HU-VPN!)
                  2. W.B.R. Lickorish:  An Introduction to Knot Theory, Springer 1997 (electronically available)
                  3. G.Burde, H.Zieschang, M.Heusener: Knots. De Gruyter 2014 (electronically available)
                  4. M.A.Armstrong: Basic Topology. Springer 1983 (electronically available)
                  5. Ch. Livingston: Knot Theory. MAA 1993 (electronically available, also in German)
                  6. V.V. Prasolov, A.B. Sossinsky: Knots, Links, Braids and 3-Manifolds. AMS 1991 (electronically availabe)
                  7. C.C. Adams: On Knots, AMS 2004 (no electronic version available)
                 

There are many more (have a look in the library catalogue). These two contain discussions of proofs of fundamental results.

There is a class on 3-Manifolds by Marc Kegel which is closely related to Knot theory!

Talks

This is a list of possible subjects. The amount we will be able to cover depends on the number of students. Names of speakers are added.
Prospective dates are indicated. We need to agree on additional meetings probably.

05/06    Knots: Definition, Examples (also pathological ones), Links (Lit.: 1., 2., 3.,5.)  Todoulou
05/13    Knot diagrams (definition and existence), Reidemeister moves (including proofs) (1., 2., 3., 5.)  Huneshagen
05/20    Idea of knot invariants. Bridge and unknotting numbers (short discussion). Linking number. Tricolourability (definition, proof of invariance)(internet research) Gerlach
05/27    Knot polynomials (combinatorial definition of Alexander-Conway polynomial (and possibly the Jones polynomial)) Dawid
06/03    Seifert surfaces (Proof of existence). Genus of a knot, additivity under knot sums, prime decompositon of knots (3., 4., 5.) Levinson
06/10    Fundamental group (definition, group axioms), fundamental group of a circle  Mousseau
06/17    Knot group (representation of the fundamental group of the knot complement via knot diagrams) Đukić
06/24    Cyclic coverings and the commutator subgroup of the knot group  Mohnke
07/01    Fibered knots/links El Agami
07/08    Universal cyclic coverings, geometric definition of the Alexander polynomial
07/15    Prime decomposition and bridge number (3.)
t.b.d.     Braids, links and Markov's theorem
07/22    Knot invariants from presentation of the braid group (3.) Maravall

last changes: Tue, July 7,  5:05  p.m.