Differential Geometry
S1-bundles and gerbes over differentiable stacks
[S1-fibrés et gerbes sur des champs différentiables]

Présenté par : Charles-Michel Marle

Behrend, Kai1 ; Xu, Ping2
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, Tome 336 (2003) no. 2, pp. 163-168.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)00025-0
Behrend, Kai 1 ; Xu, Ping 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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Behrend, Kai; Xu, Ping. S1-bundles and gerbes over differentiable stacks. Comptes Rendus. Mathématique, Tome 336 (2003) no. 2, pp. 163-168. doi : 10.1016/S1631-073X(02)00025-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)00025-0/

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

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

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

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