Janis Lazovskis, Department of Pure Math, University of Waterloo
“Introducing characteristic classes”
We will begin by introducing vector and tangent bundles, cohomology groups, and other background information to motivate characteristic classes. The Euler class, essentially encoding the Euler characteristic of a manifold, will be presented as the first example of a characteristic class. The approach will be topological, following the methods presented in ”Characteristic classes” by Milnor and Stasheff. Hopefully the groundwork will be laid for a detailed analysis of Chern and Stiefel-Whitney classes later, through both topology and differential geometry, by way of connections.