Higher-twisted periodic smooth deligne cohomology

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticlepeer-review


Generalizing degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, from previous work, here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree.We present the main properties of the new theory and illustrate its use with examples and computations, mainly via a corresponding twisted differential Atiyah-Hirzebruch spectral sequence.

Original languageEnglish (US)
Pages (from-to)129-159
Number of pages31
JournalHomology, Homotopy and Applications
Issue number1
StatePublished - 2019


  • Atiyah-Hirzebruch spectral sequence
  • Deligne cohomology
  • Differential cohomology
  • Gerbe
  • Stack
  • Twisted cohomology

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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