Equivariant Dixmier-Douady Classes

Abstract

An equivariant bundle gerbe à la Meinrenken over a $G$-manifold $M$ is known to be a special type of $S^1$-gerbe over the differentiable stack $[M/G]$. We prove that the natural morphism relating the Cartan and simplicial models of equivariant cohomology in degree 3 maps the Dixmier-Douady class of an equivariant bundle gerbe à la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding $S^1$-gerbe.

18 pages

References in corpus (1)

• Differentiable Stacks and Gerbes

Cited by in corpus (5)

• Non Abelian Differentiable Gerbes
• Differentiable Stacks and Gerbes
• Multiplicative vector fields on bundle gerbes
• Basic equivariant gerbes on non-simply connected compact simple Lie groups
• Periodic Cyclic Homology and Equivariant Gerbes