Differentiable stacks and gerbes
type: Item
instance of: scholarly article
title: Differentiable stacks and gerbes
zbMATH Open document ID: 1227.14007
author: Ping Xu
author: Kai Behrend
published in: The Journal of Symplectic Geometry
publication date: 2011-10-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0605694
full work available at URL: https://projecteuclid.org/euclid.jsg/1310388899
review text: In this article, which is seen as a continuation of the work ``\(S^1\)-bundles and gerbes over differentiable stacks'' [C. R., Math., Acad. Sci. Paris 336, No. 2, 163--168 (2003; Zbl 1039.58016)] studied by the same authors, the authors present a large background related to differentiable stacks and gerbes. The main purpose of the article is to develop the theory of \(S^1\)-gerbes over differentiable stacks. The work has based on relationship between Lie groupoids and differentiable stacks which has a large application area in different branches of mathematics such as algebraic geometry, differential geometry and differential topology, etc. Specially, the authors show that \(S^1\)-gerbes are in one-to-one correspondence with Morita equivalence classes of groupoid \(S^1\)-central extensions. Also, they show that pseudo-connections can be used to calculate Dixmier-Douady classes. At the end of the work, they give a construction of \(S^1\)-central extensions with the pseudo-curvature.
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 53C08
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 58H05
zbMATH DE Number: 5956509
zbMATH Keywords: differentiable stack
zbMATH Keywords: gerb
zbMATH Keywords: Lie groupoid
zbMATH Keywords: central extension
reviewed by: M. Habil Gürsoy
MaRDI profile type: Publication
arXiv ID: math/0605694
DOI: 10.4310/JSG.2011.V9.N3.A2
description: scientific article