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2017 Spectral sequences in smooth generalized cohomology
Daniel Grady, Hisham Sati
Algebr. Geom. Topol. 17(4): 2357-2412 (2017). DOI: 10.2140/agt.2017.17.2357

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.

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Daniel Grady. Hisham Sati. "Spectral sequences in smooth generalized cohomology." Algebr. Geom. Topol. 17 (4) 2357 - 2412, 2017. https://doi.org/10.2140/agt.2017.17.2357

Information

Received: 3 June 2016; Revised: 11 October 2016; Accepted: 3 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1375.55002
MathSciNet: MR3686400
Digital Object Identifier: 10.2140/agt.2017.17.2357

Subjects:
Primary: 55N15, 55T10, 55T25
Secondary: 53C05, 55S05, 55S35

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 4 • 2017
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