Contents Online
Mathematical Research Letters
Volume 17 (2010)
Number 1
Equivariant Dixmier-Douady Classes
Pages: 127 – 145
DOI: https://dx.doi.org/10.4310/MRL.2010.v17.n1.a10
Author
Abstract
An equivariant bundle gerbe \`a 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 \`a la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding $S^1$-gerbe.
Published 1 January 2010