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Differential Topology

This seminar is intended for students who have completed the courses Analysis 1-3.

Sommersemester 2014

Dozent:  Prof. Dr. Elmar VogtDr. Fabian Lenhardt

Ort: Seminarraum 005, Arnimallee 3

Literature

We plan to work through the small book "Topology from the Differential Viewpoint" by John Milnor, one of the Classics of the Princeton University Press and a mathematical jewel. It introduces the reader to some fundamental concepts of early topology, but instead of using algebraic and combinatorial tools it uses elementary methods from real analysis, also introducing some basic concepts of differential topology like differential manifolds, tangent bundles and vector fields.

Talks

TerminTitelVortragende(r)Referenzen

24.4.

(1) Prerequisites    

8.5.

(2) Regular Values    

15.5.

(3) Sard's theorem    

22.5.

(4) Degree mod 2    

5.6.

(5) Brouwer degree    

12.6.

(6) Vector fields and Euler characteristic    

19.6.

(7) Vector fields and Euler characteristic II    

26.6.

(8) The Pontrjagin-Thom construction    

17.6.

(9) The Pontrjagin-Thom construction