Twisted smooth Deligne cohomology

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticle

Abstract

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful.

Original languageEnglish (US)
Pages (from-to)445-466
Number of pages22
JournalAnnals of Global Analysis and Geometry
Volume53
Issue number3
DOIs
StatePublished - Apr 1 2018

Keywords

  • Connections
  • Deligne cohomology
  • Differential cohomology
  • Local coefficient systems
  • Smooth stacks
  • Twisted cohomology
  • Čech-de Rham complex

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology

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