A classification of equivariant gerbe connections

Park, Byungdo; Redden, Corbett

doi:10.1142/S0219199718500013

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A classification of equivariant gerbe connections

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Park, Byungdo
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.1142/S0219199718500013
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arXiv:1709.06003.pdf
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Park, B., & Redden, C. (2019). A classification of equivariant gerbe connections. Communications in Contemporary Mathematics, 21(2): 1850001. doi:10.1142/S0219199718500013.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6831-0

Abstract

Let G be a compact Lie group acting on a smooth manifold M. In this paper, we consider Meinrenken's G-equivariant bundle gerbe connections on M as objects in a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe connections on the differential quotient stack associated to M, and isomorphism classes of G-equivariant gerbe connections are classified by degree 3 differential equivariant cohomology. Finally, we consider the existence and uniqueness of conjugation-equivariant gerbe connections on compact semisimple Lie groups.