Topology and Geometry Seminar

Location: CL 416

Speaker: Martin Frankland, University of Regina

Title: Stiefel-Whitney classes, an axiomatic approach

Abstract:  

In the previous talks, we constructed the first Stiefel-Whitney class of a real vector bundle and argued that it is the obstruction to orientability. In this talk, we will introduce higher Stiefel-Whitney classes, which are invariants of a vector bundle living in the cohomology of the base space. Postponing an explicit construction, we will assume that the Stiefel-Whitney classes satisfy four axioms. From there, we will deduce some computations and applications, for instance to embeddings of manifolds.