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 | Date | Reference | ||
| 1 | Constructing New Vector Bundles | 09.10.2019 | Chunqiu | MS §3 |
| 2 | Stiefel-Whitney Classes 1 | 16.10.2019 | Matthias | MS §4 |
| 3 | Stiefel-Whitney Classes 2 | 23.10.2019 | Jonah | MS §4 |
| 4 | Grassmann Manifolds | 30.10.2019 | Janik | MS §5 |
| 5 | A Cell Structure for Grassmann Manifolds | 06.11.2019 | Diao | MS §6 |
| 6 | The Cohomology Ring of Grassmann Manifolds | 13.11.2019 | Antonio | MS §7 |
| 7 | Oriented Bundles and the Euler Class | 20.11.2019 | Cara | MS §9 |
| 8 | The Thom Isomorphism Theorem | 27.11.2019 | Christian | MS §10 |
| 9 | Existence of Stiefel-Whitney Classes | 04.12.2019 | Rui | Kreck Ch. 17, MS §8 |
| 10 | Computations in a Smooth Manifold 1 | 06.12.2019 | Liao | MS §11 |
| 11 | Computations in a Smooth Manifold 2 | 11.12.2019 | Frieder | MS §11 |
| 12 | Obstructions | 13.12.2019 | Jacobus | MS §12 |
| 13 | Chern Classes | 18.12.2019 | Hao | Kreck Ch. 17, MS §13,14 |
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