Title: Describing principal bundles and pushing TQFTs forward
Abstract: In the first part of this talk we will discuss several ways, how principal bundles over a manifold can be described. The main two of them are maps from the base manifold into the group’s classifying space and assignments of group elements to the codimension one structures of a special decomposition, called fine stratification. Both of them provide an equivalence of categories to the category of principal bundles. Having all these equivalent descriptions, one can translate geometric constructions with principal bundles into discrete combinatorial constructions. In the second part of this talk I will outline, starting from a pushforward construction for equivariant Topological Quantum Field Theories, how this can be used to define a pushforward construction for defect Topoplogical Quantum Field Theories.
This is joint work with Gregor Schaumann, as part of my Master’s project.