A classification of equivariant gerbe connections

TL;DR

This paper classifies G-equivariant bundle gerbe connections on manifolds using differential equivariant cohomology and establishes their equivalence with gerbe connections on differential quotient stacks, also exploring conjugation-equivariant cases.

Contribution

It proves the 2-category of G-equivariant gerbe connections is equivalent to that on the quotient stack and classifies isomorphism classes via differential equivariant cohomology.

Findings

Equivalence of 2-groupoids of equivariant and stack-based gerbe connections

Classification of isomorphism classes by degree three differential equivariant cohomology

Existence and uniqueness results for conjugation-equivariant gerbe connections on compact semisimple Lie groups

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 three differential equivariant cohomology. Finally, we consider the existence and uniqueness of conjugation-equivariant gerbe connections on compact semisimple Lie groups.