String structures, 2-group bundles, and a categorification of the Freed-Quinn line bundle

Daniel Berwick-Evans, Emily Cliff, Laura Murray,Apurva Nakade, Emma Phillips

arXiv (Cornell University)(2021)

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Abstract
For a 2-group constructed from a finite group and 3-cocycle, we provide an explicit description of the bicategory of flat 2-group bundles on an oriented surface in terms of weak representations of the fundamental group. We show that this bicategory encodes (flat) string structures. Furthermore, we identify the space of isomorphism classes of objects with Freed and Quinn's line bundle appearing in Chern-Simons theory of a finite group.
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Key words
categorification,structures,freed-quinn
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