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A classification of equivariant gerbe connections

Byungdo Park

School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea

E-mail Address: [email protected]

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and

Corbett Redden

Department of Mathematics, LIU Post, Long Island University, 720 Northern Blvd., Brookville, NY 11548, USA

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219199718500013Cited by: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.

Keywords:

AMSC: 53C08, 55R65, 55R91

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Vol. 21, No. 02

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History

Received 10 November 2017

Revised 19 December 2017

Accepted 21 December 2017

Published: 7 March 2018

Keywords

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A classification of equivariant gerbe connections

Abstract

References

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