Higher-twisted periodic smooth deligne cohomology

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticle

Abstract

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
Volume21
Issue number1
DOIs
StatePublished - Jan 1 2019

Fingerprint

Twist
Cohomology
Odd
Gerbe
De Rham Cohomology
Michael Francis Atiyah
Spectral Sequence
Refinement
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Higher-twisted periodic smooth deligne cohomology. / Grady, Daniel; Sati, Hisham.

In: Homology, Homotopy and Applications, Vol. 21, No. 1, 01.01.2019, p. 129-159.

Research output: Contribution to journalArticle

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