Characteristic Classes

Hopf's 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 computing examples.