Mathematical Research Letters

Volume 17 (2010)

Number 1

Equivariant Dixmier-Douady Classes

Pages: 127 – 145

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n1.a10

Author

Mathieu Stiénon (E.T.H. Zürich)

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.

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