Spectral sequences in smooth generalized cohomology

Daniel Grady, Hisham Sati

Research output: Contribution to journalArticle

Abstract

We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be of the Atiyah-Hirzebruch (AHSS) type, where we provide a filtration by the Čech resolution of smooth manifolds. This allows for systematic study of torsion in differential cohomology. We apply this in detail to smooth Deligne cohomology, differential topological complex K-theory and to a smooth extension of integral Morava K-theory that we introduce. In each case, we explicitly identify the differentials in the corresponding spectral sequences, which exhibit an interesting and systematic interplay between (refinements of) classical cohomology operations, operations involving differential forms and operations on cohomology with U(1) coefficients.

Original languageEnglish (US)
Pages (from-to)2357-2412
Number of pages56
JournalAlgebraic and Geometric Topology
Volume17
Issue number4
DOIs
StatePublished - Aug 3 2017

Fingerprint

Spectral Sequence
Cohomology
Morava K-theory
Michael Francis Atiyah
Smooth Manifold
Differential Forms
K-theory
Filtration
Torsion
Refinement
Coefficient

Keywords

  • Atiyah-Hirzebruch spectral sequence
  • Cohomology operations
  • Differential cohomology
  • Generalized cohomology
  • Smooth cohomology

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Spectral sequences in smooth generalized cohomology. / Grady, Daniel; Sati, Hisham.

In: Algebraic and Geometric Topology, Vol. 17, No. 4, 03.08.2017, p. 2357-2412.

Research output: Contribution to journalArticle

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