Primary operations in differential cohomology

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticle

Abstract

We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a delicate interplay between integral, rational, and mod p cohomology, as well as cohomology with U(1) coefficients and differential forms. Along the way we develop computational techniques in differential cohomology, including a Künneth decomposition, that should also be useful in their own right, and point to applications to higher geometry and mathematical physics.

Original languageEnglish (US)
Pages (from-to)519-562
Number of pages44
JournalAdvances in Mathematics
Volume335
DOIs
StatePublished - Sep 7 2018

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Cohomology
Higher geometry
Computational Techniques
Differential Forms
Physics
Decompose
Coefficient

Keywords

  • Cohomology operations
  • Deligne cohomology
  • Differential cohomology
  • Gerbes
  • Stacks
  • Steenrod squares

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Primary operations in differential cohomology. / Grady, Daniel; Sati, Hisham.

In: Advances in Mathematics, Vol. 335, 07.09.2018, p. 519-562.

Research output: Contribution to journalArticle

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