Groupoid Cohomology and the Dixmier-Douady Class
نویسندگان
چکیده
منابع مشابه
Principal Bundles and the Dixmier Douady Class
A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the DixmierDouady class in various contexts including string structures, Ures bundles and other examples motivated by considerations from quantum field theory.
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An equivariant bundle gerbe à la Meinrenken over a G-manifold M is known to be a special type of S-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 à la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding S-g...
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We show that Haefliger’s cohomology for étale groupoids, Moore’s cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (or Čech) cohomology for topological simplicial spaces.
متن کامل4 Groupoid Cohomology and Extensions
We show that Haefliger's cohomology forétale groupoids, Moore's cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (oř Cech) cohomology for topological simplicial spaces.
متن کاملAn index for gauge-invariant operators and the Dixmier-Douady invariant
Let G → B be a bundle of compact Lie groups acting on a fiber bundle Y → B. In this paper we introduce and study gauge-equivariant K-theory groups K G(Y ). These groups satisfy the usual properties of the equivariant K-theory groups, but also some new phenomena arise due to the topological non-triviality of the bundle G → B. As an application, we define a gauge-equivariant index for a family of...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1995
ISSN: 0024-6115
DOI: 10.1112/plms/s3-71.1.109