EQUIVARIANT DIXMIER-DOUADY CLASSES

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.