Topology and Geometry Seminar

Location: CL 416

Speaker: Matthew Alexander, University of Regina

Title: Classifying Spaces

Abstract:  

In this talk we will look at how the classification of principal bundles can be reduced to looking at maps into certain classifying spaces. We will give a simplicial construction of these spaces, and then introduce Grassmannians and show how the classifying spaces of O(n) and U(n) principal bundles arise as colimits of Grassmannians. Finally, we will see how the cohomology ring of certain classifying spaces ties into the Chern and Stiefel-Whitney classes that we have already seen.