Hadrien Chalandon--Goskrzynski: An Introduction to Characteristic Classes

Abstract

Stiefel-Whitney classes are algebraic invariants that are used to study vector bundles. In this talk, I will attempt to give an introduction to these classes and show why they are interesting. No prior knowledge of algebraic topology is assumed. As such, I will introduce singular (co-) homology, vector bundles, and then move on to Stiefel-Whitney classes, of which I will give several applications. I'll also mention universal bundles and how they are used to define characteristic classes in a much more general fashion.