Equivariant Dixmier-Douady classes

Mathieu Stiénon

doi:10.4310/MRL.2010.v17.n1.a10

Equivariant Dixmier-Douady classes

Mathieu Stiénon

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

An equivariant bundle gerbe ̀a la Meinrenken over a G-manifold M is known to be a special type of S¹-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 S¹-gerbe.

Original language	English (US)
Pages (from-to)	127-145
Number of pages	19
Journal	Mathematical Research Letters
Volume	17
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2010.v17.n1.a10
State	Published - Jan 2010

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Equivariant Dixmier-Douady classes",

abstract = "An equivariant bundle gerbe{\` }a la Meinrenken over a G-manifold M is known to be a special type of S1-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 S1-gerbe.",

author = "Mathieu Sti{\'e}non",

year = "2010",

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doi = "10.4310/MRL.2010.v17.n1.a10",

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AB - An equivariant bundle gerbe ̀a la Meinrenken over a G-manifold M is known to be a special type of S1-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 S1-gerbe.

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DO - 10.4310/MRL.2010.v17.n1.a10

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JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 1

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Equivariant Dixmier-Douady classes

Abstract

All Science Journal Classification (ASJC) codes

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