QG group meeting: Non-Hausdorff Vector Bundles (Part 2)

QG group meeting.
Speaker: David O'Connell.
Title: Non-Hausdorff Vector Bundles (Part 2).

Abstract: In the last talk we saw that all non-Hausdorff manifolds are secretly “colimits”, which was a fancy category-theory term for gluing things together. We also saw that all the non-Hausdorff vector bundles can be similarly constructed. In this talk we will repeat this idea one more time and study various structures that one may associate to a manifold. In particular, we will create formulas for the ring of smooth functions over a non-Hausdorff manifolds and the sections of arbitrary non-Hausdorff vector bundles. Time permitting, we will also classify the real non-Hausdorff line bundles in terms of Cech cohomology.