Non-abelian differentiable gerbes

Camille Laurent-Gengoux, Mathieu Philippe Stienon, Ping Xu

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid G-extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi identities. In particular, we develop a cohomology theory which measures the existence of connections and curvings for G-gerbes over stacks. We also introduce G-central extensions of groupoids, generalizing the standard groupoid S1-central extensions. As an example, we apply our theory to study the differential geometry of G-gerbes over a manifold.

Original languageEnglish (US)
Pages (from-to)1357-1427
Number of pages71
JournalAdvances in Mathematics
Volume220
Issue number5
DOIs
StatePublished - Mar 20 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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