PIRSA:24050078

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

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

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

          @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

DOI 10.48660/24050078
Collection
Talk Type Scientific Series
Subject

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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