Equivariant Dixmier-Douady Classes

Details Equivariant Dixmier-Douady Classes Equivariant Dixmier-Douady Classes

2007-09-17

arxiv.org/abs/0709.2720v1

Math. Res. Lett. 17 (2010), no. 1, 127-145

Mathematics

Differential Geometry

18 pages

Scientific paper

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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