Differential Geometry Working Seminar

Paul Cusson, Department of Pure Mathematics, University of Waterloo

"Infinite Flag Manifolds and Vector Bundle Filtrations"

In this talk we will look at infinite flag manifolds as classifying spaces of vector bundle filtrations, which generalizes the classifying property of infinite Grassmannians for vector bundles. The main tool for this study is the fact that real and complex flag manifolds are in general iterated fiber bundles with Grassmannian components. As such, this allows one to efficiently write down the homotopy groups and cohomology rings of flag manifolds in terms of those of the Grassmannians. Bundle extension problems and obstruction theoretic results will be looked at if time allows.

MC 5403