# Principal 2-group bundles and the Freed--Quinn line bundle

### APA

Cliff, E. (2024). Principal 2-group bundles and the Freed--Quinn line bundle. Perimeter Institute. https://pirsa.org/24050078

### MLA

Cliff, Emily. Principal 2-group bundles and the Freed--Quinn line bundle. Perimeter Institute, May. 16, 2024, https://pirsa.org/24050078

### BibTex

@misc{ pirsa_PIRSA:24050078, doi = {10.48660/24050078}, url = {https://pirsa.org/24050078}, author = {Cliff, Emily}, keywords = {Mathematical physics}, language = {en}, title = {Principal 2-group bundles and the Freed--Quinn line bundle}, publisher = {Perimeter Institute}, year = {2024}, month = {may}, note = {PIRSA:24050078 see, \url{https://pirsa.org}} }

Emily Cliff University of Sherbrooke

## Abstract

A 2-group is a categorical generalization of a group: it's a category with a multiplication operation which satisfies the usual group axioms only up to coherent isomorphisms. The isomorphism classes of its objects form an ordinary group, G. Given a 2-group **G **with underlying group G, we can similarly define a categorical generalization of the notion of principal bundles over a manifold (or stack) X, and obtain a bicategory Bun_**G**(X), living over the category Bun_G(X) of ordinary G-bundles on X. For G finite and X a Riemann surface, we prove that this gives a categorification of the *Freed--Quinn line bundle*, a mapping-class group equivariant line bundle on Bun_G(X) which plays an important role in Dijkgraaf--Witten theory (i.e. Chern--Simons theory for the finite group G). This talk is based on joint work with Daniel Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips.

I will not assume previous knowledge of 2-groups: I will provide a quick overview in the main talk, as well as a more detailed discussion during a pre-talk on Tuesday.

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