Characteristic classes as obstructions
Event details
| Date | 27.09.2016 |
| Hour | 10:15 › 11:30 |
| Speaker | Martina Rovelli (EPFL) |
| Location |
CM 113
|
| Category | Conferences - Seminars |
Characteristic classes are invariants for principal bundles that take values in the cohomology of the base space. Every characteristic class captures different geometric features of principal bundles. It is known, for instance, that the first Stiefel-Whitney class of an O(n)-bundle vanishes if and only if the bundle is orientable, in which case the structure group can be reduced to SO(n). In the first part of this talk, we propose a uniform treatment to interpret most of the studied characteristic classes as an obstruction to group reduction. By plugging in the correct parameters, the method recovers several classical theorems. Afterwards, I will explain how the main result leads to the construction of a long exact sequence of abelian groups for any principal bundle. This sequence involves the cohomology of the base space and the group cohomology of the structure group, and the connecting map is deeply related with the characteristic classes of the bundle.
Links
Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek