Differential cocycles and Dixmier–Douady bundles

Derek Krepski, Jordan Watts

Research output: Contribution to journalArticlepeer-review

Abstract

This paper exhibits equivalences of 2-stacks between certain models of S1-gerbes and differential 3-cocycles. We focus primarily on the model of Dixmier–Douady bundles, and provide an equivalence between the 2-stack of Dixmier–Douady bundles and the 2-stack of differential 3-cocycles of height 1, where the ‘height’ is related to the presence of connective structure. Differential 3-cocycles of height 2 (resp. height 3) are shown to be equivalent to S1-bundle gerbes with connection (resp. with connection and curving). These equivalences extend to the equivariant setting of S1-gerbes over Lie groupoids, and can be applied to the setting of S1-gerbes over orbifolds.

Original languageEnglish
Pages (from-to)168-183
Number of pages16
JournalJournal of Geometry and Physics
Volume130
DOIs
StatePublished - Aug 2018

Keywords

  • Differential character
  • Differential cocycle
  • Dixmier–Douady bundle
  • Dixmier–Douady class
  • Gerbe
  • Stack

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