Responsible: Christian Bär

The classical Hairy Ball Theorem states that on a compact surface with nontivial Euler number there are no nowhere vanishing continuous vector fields. This is a prototypical application of characteristic classes: a cohomology class (here: the Euler class) measures the nontriviality of a vector bundle (here: the tangent bundle). The course will provide a systematic introduction to characteristic classes. Along the way, we will learn how to use the computer algebra system Sage to facilitate the computation of examples. We will treat the following topics:

• Fundamentals to the extent necessary (vector bundles, deRham cohomology)
• Chern classes, Pontryagin classes, Euler class
• Secondary classes (Chern-Simons class)
• Applications

The lecture course will be held in English. The course will held in a hybrid mode meaning that you can attend in person or by video stream. It will start on October 25, 2021.

If you are interested, please register without obligation in this moodle. There you will find all further information. If you do not have a uni-potsdam email address, you first have to sign up for a moodle account for external participants.

Prior knowledge:
You need to know manifolds and differential forms, e.g. the Stokes theorem. Vector bundles will introduced in the beginning of the course if necessary. Knowledge of Sage is not required.