Moduli spaces of principal 2-group bundles and a categorification of the Freed-Quinn line bundle

Emily Cliff (Université de Sherbrooke)

03-May-2022, 14:00-15:00 (23 months ago)

Abstract: A 2-group is a higher categorical analogue of a group, while a smooth 2-group is a higher categorical analogue of a Lie group. An important example is the string 2-group in the sense of Schommer-Pries. We study the notion of principal bundles for smooth 2-groups, and investigate the moduli "space" of such objects. In particular, in the case of flat principal bundles for a finite 2-group over a Riemann surface, we prove that the moduli space gives a categorification of the Freed--Quinn line bundle. This line bundle has as its global sections the state space of Chern-Simons theory for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studied by Waldorf and Stolz-Teichner).

The talk will not assume background knowledge on 2-groups or Chern-Simons theory. It is based on joint work with Dan Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic


The TRAC Seminar - Théorie de Représentations et ses Applications et Connections

Organizers: Thomas Brüstle*, Souheila Hassoun
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