S4D2 – Graduate Seminar on Topology - Characteristic Classes

Winter term 2019/20

Daniel Kasprowski, Wolfgang Lück and Julia Semikina

Wednesday 10:15 - 12:00; seminar room N 0.007
The extra dates are Friday 14:15-16:00; Zeichensaal

The organizational meeting takes place Friday, July 5th at 3:15pm in Kleiner Hörsaal.

The seminar will mainly follow the book Characteristic Classes by Milnor and Stasheff. For the construction of the Stiefel-Whitney and Chern classes we follow Differential Algebraic Topology by Kreck. We assume basic knowledge about smooth manifolds, vector bundles, and homology and homotopy groups.

We plan to continue the seminar in the summer term 2020 to see interesting applications of characteristic classes.

Topic DateReference
1 Constructing New Vector Bundles 09.10.2019ChunqiuMS §3
2 Stiefel-Whitney Classes 1 16.10.2019MatthiasMS §4
3 Stiefel-Whitney Classes 2 23.10.2019JonahMS §4
4 Grassmann Manifolds 30.10.2019JanikMS §5
5 A Cell Structure for Grassmann Manifolds 06.11.2019DiaoMS §6
6 The Cohomology Ring of Grassmann Manifolds 13.11.2019AntonioMS §7
7 Oriented Bundles and the Euler Class 20.11.2019CaraMS §9
8 The Thom Isomorphism Theorem 27.11.2019ChristianMS §10
9 Existence of Stiefel-Whitney Classes 04.12.2019RuiKreck Ch. 17, MS §8
10 Computations in a Smooth Manifold 1 06.12.2019LiaoMS §11
11 Computations in a Smooth Manifold 2 11.12.2019FriederMS §11
12 Obstructions 13.12.2019JacobusMS §12
13 Chern Classes 18.12.2019HaoKreck Ch. 17, MS §13,14