Differential geometry of gerbes

Lawrence Breen, William Messing

Research output: Contribution to journalArticle

65 Scopus citations

Abstract

We define in a global manner the notion of a connective structure for a gerbe on a space X. When the gerbe is endowed with trivializing data with respect to an open cover of X, we describe this connective structure in two separate ways, which extend from abelian to general gerbes the corresponding descriptions due to J.-L. Brylinski and N. Hitchin. We give a global definition of the 3-curvature of this connective structure as a 3-form on X with values in the Lie stack of the gauge stack of the gerbe. We also study this notion locally in terms of more traditional Lie algebra-valued 3-forms. The Bianchi identity, which the curvature of a connection on a principal bundle satisfies, is replaced here by a more elaborate equation.

Original languageEnglish (US)
Pages (from-to)732-846
Number of pages115
JournalAdvances in Mathematics
Volume198
Issue number2 SPEC. ISS.
DOIs
StatePublished - Dec 20 2005

Keywords

  • 3-Curvature
  • Connection
  • Gerbe
  • Non-abelian cohomology

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    Breen, L., & Messing, W. (2005). Differential geometry of gerbes. Advances in Mathematics, 198(2 SPEC. ISS.), 732-846. https://doi.org/10.1016/j.aim.2005.06.014