<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

@article{CRMATH_2003__336_2_163_0,
     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},
     volume = {336},
     number = {2},
     year = {2003},
     doi = {10.1016/S1631-073X(02)00025-0},
     language = {en},
}

TY  - JOUR
AU  - Kai Behrend
AU  - Ping Xu
TI  - S1-bundles and gerbes over differentiable stacks
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 163
EP  - 168
VL  - 336
IS  - 2
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)00025-0
LA  - en
ID  - CRMATH_2003__336_2_163_0
ER  -

%0 Journal Article
%A Kai Behrend
%A Ping Xu
%T S1-bundles and gerbes over differentiable stacks
%J Comptes Rendus. Mathématique
%D 2003
%P 163-168
%V 336
%N 2
%I Elsevier
%R 10.1016/S1631-073X(02)00025-0
%G en
%F CRMATH_2003__336_2_163_0

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

[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

Cité par Sources :

Commentaires - Politique