<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
[S¹-fibrés et gerbes sur des champs différentiables]

Présenté par : 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.

Résumé
Abstract

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 : 2002-09-24
Accepté le : 2002-12-02
Publié le : 2003-01-15

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

Affiliations des auteurs :

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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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/

Bibliographie
Cité par

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

Antonio Maglio; Alfonso Giuseppe Tortorella; Luca Vitagliano Shifted Contact Structures on Differentiable Stacks, International Mathematics Research Notices, Volume 2024 (2024) no. 16, p. 11933 | DOI:10.1093/imrn/rnae144
Camille Laurent-Gengoux; Mathieu Stiénon; Ping Xu Non-abelian differentiable gerbes, Advances in Mathematics, Volume 220 (2009) no. 5, p. 1357 | DOI:10.1016/j.aim.2008.10.018
Giovanni Felder; André Henriques; Carlo A. Rossi; Chenchang Zhu A gerbe for the elliptic gamma function, Duke Mathematical Journal, Volume 141 (2008) no. 1 | DOI:10.1215/s0012-7094-08-14111-0
Christian Blohmann Stacky Lie Groups, International Mathematics Research Notices, Volume 2008 (2008) | DOI:10.1093/imrn/rnn082
Camille Laurent-Gengoux; Jean-Louis Tu; Ping Xu Chern–Weil map for principal bundles over groupoids, Mathematische Zeitschrift, Volume 255 (2007) no. 3, p. 451 | DOI:10.1007/s00209-006-0004-4
Camille Laurent-Gengoux; Ping Xu Quantization of pre-quasi-symplectic groupoids and their Hamiltonian spaces, The Breadth of Symplectic and Poisson Geometry, Volume 232 (2007), p. 423 | DOI:10.1007/0-8176-4419-9_14
Jean-Louis Tu; Ping Xu Chern character for twisted K-theory of orbifolds, Advances in Mathematics, Volume 207 (2006) no. 2, p. 455 | DOI:10.1016/j.aim.2005.12.001
Kai A. Behrend On the de Rham cohomology of differential and algebraic stacks, Advances in Mathematics, Volume 198 (2005) no. 2, p. 583 | DOI:10.1016/j.aim.2005.05.025

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