QG group meeting: Non-Hausdorff Vector Bundles (Part 1)

QG group meeting.
Speaker: David O'Connell.
Title: Non-Hausdorff Vector Bundles (Part 1).

Abstract: In these two talks we will introduce some global features of non-Hausdorff differential geometry. In this, the first talk, we will start by recalling the basic formalism of non-Hausdorff manifolds. We will lean on some notions from topology and category theory, so these will also be introduced. Eventually we will get to the conclusion that all non-Hausdorff manifolds can be built by gluing together ordinary Hausdorff ones, and all vector bundles can be constructed in an analogous manner. These gluing constructions make non-Hausdorff manifolds much more tractable, and therefore much less scary.