涩里番

Title: Classifying principal bundles for smooth 2-groups

Abstract: A 2-group is a categorified version of a group: a category with a multiplication operator, for which all group axioms hold up to natural isomorphism. Similarly, there is a notion of a smooth 2-group, and of principal 2-group bundles. We classify 2-group bundles in terms of 膶ech data or transition functions, which enables us to give a concrete description of the moduli space of principal 2-group bundles.

In the case of a finite 2-group, we prove that this moduli space gives a 2-fibration over the moduli space of flat principal bundles for an ordinary finite group, and provides a categorification of the Freed鈥換uinn line bundle, a mapping-class-group-equivariant line bundle arising in Dijkgraaf鈥揥itten theory for the finite group. We expect analogous results to hold in the smooth setting, with applications to the Chern-Simons theory of a Lie group. This is joint work with Daniel Berwick-Evans and Laura Murray.

Location: UQAM PK-5675