<i>S</i><sup>1</sup>-bundles and gerbes over differentiable stacks

Kai Behrend; Ping Xu

doi:10.1016/S1631-073X(02)00025-0

Differential Geometry

S¹-bundles and gerbes over differentiable stacks

Presented by: Charles-Michel Marle

Kai Behrend ¹; Ping Xu ²

¹ Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver BC, V6T IZ2, Canada
² Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 163-168.

Abstract
Résumé

We study S¹-bundles and S¹-gerbes over differentiable stacks in terms of Lie groupoids, and construct Chern classes and Dixmier–Douady classes in terms of analogues of connections and curvature.

Nous étudions les S¹-fibrés et les S¹-gerbes sur des champs différentiables en termes de groupoı̈des de Lie et nous construisons les classes de Chern et Dixmier–Douady en termes d'analogues des connexions et de leur courbure.

Received: 2002-09-24
Accepted: 2002-12-02
Published online: 2003-01-15

DOI: 10.1016/S1631-073X(02)00025-0

Author's affiliations:

Kai Behrend ¹; Ping Xu ²

¹ Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver BC, V6T IZ2, Canada
² Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

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     author = {Kai Behrend and Ping Xu},
     title = {\protect\emph{S}\protect\textsuperscript{1}-bundles and gerbes over differentiable stacks},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {163--168},
     publisher = {Elsevier},
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     doi = {10.1016/S1631-073X(02)00025-0},
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Kai Behrend; Ping Xu. S¹-bundles and gerbes over differentiable stacks. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 163-168. doi : 10.1016/S1631-073X(02)00025-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00025-0/

References
Cited by

[1] N. Hitchin Lectures on special Lagrangian submanifolds, AMS/IP Stud. Adv. Math., 23, American Mathematical Society, Providence, RI, 2001, pp. 151-182

[2] M.K. Murray Bundle gerbes, J. London Math. Soc. (2), Volume 54 (1996), pp. 403-416

[3] A. Weinstein; P. Xu Extensions of symplectic groupoids and quantization, J. Reine Angew. Math., Volume 417 (1991), pp. 159-189

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