Analysis and Geometry on Manifolds

  Th 9-11 a.m., RUD25, 1.013; Th 1-3 p.m., RUD26, 1'304

German version


Lecturer
:           Klaus Mohnke
                           Office: Adlershof, Haus 1,  Zimmer 306
                           phone: (030) 2093 1814
                           fax: (030) 2093 2727
                           email:   mohnke@mathematik.hu-berlin.de
 

Tutorial:  Wed 9-11, RUD 25, 3.007, Klaus Mohnke
                  Th 11-1p.m., RUD 25, 3.008 (except on Nov 9: 1.315 !!), Nicolas Roy           
 

Office hours: Wed 11 a.m. - 1 p.m., RUD25, 1.304 (office) and by appointment



Homework

Homework Set 1
Homework Set 2
Homework Set 3
Homework Set 4
Homework Set 5
Homework Set 6
Homework Set 7
Homework Set 8
Homework Set 9
Homework Set 10
Homework Set 11
Homework Set 12
Homework Set 13
Homework Set 14



Grading

Results



Solutions to some problems

CP1and  S2 are diffeomorphic (Homework Set 1)
Flows of commuting vector fields commute (Homework Set 3)





Current and past  subjects of the class:
 

          Definition (Atlases, differential structure, parametrizations, charts and coordinates,
                             transition functions, examples)
          Topology (open and closed sets, neighbourhoods, continuous functions, Hausdorff spaces)
          Tangent space (physicists, geometric and algebraic definition)
          Vector fields (Lie bracket, flows, Lie derivative)
          Submanifolds (immersions, embeddings, examples, tangent spaces)
          Quotient spaces (discrete group actions)
Literature:

Manifolds:
  1. M.P.do Carmo: Riemannian Geometry, Birkäuser1992
  2. V.Guillemin,A.Pollack: Differential Topology, Prentice-Hall 1974
  3. John Lee: Introduction to smooth manifolds, Springer
Differential forms and Stokes' Theorem:
  1. I.Agricola,Th.Friedrich: Globale Analysis, Vieweg 2001
  2. M.Spivak: Calculus on Manifolds, Addison-Wesley 1965
  3. M.P.do Carmo: Differential Forms and Applications, Springer 1994
  4. O.Forster: Ana;ysis 3. Integralrechnnung im Rn mit Anwendungen, Vieweg 1989





Klaus Mohnke
Fri, December 1,   2006, 3:30 p.m.