Spectral sequences in smooth generalized cohomology

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 Cech 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 (refinement of) classical cohomology operations, operations involving differential forms, and operations on cohomology with U(1) coefficients.

60 pages, published version

References in corpus (3)

• D-Branes, RR-Fields and Duality on Noncommutative Manifolds
• Primary operations in differential cohomology
• Refinements of the Chern-Dold Character: Cocycle Additions in Differential Cohomology

Cited by in corpus (8)

• Ramond-Ramond fields and twisted differential K-theory
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Primary operations in differential cohomology
• Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
• Twisted smooth Deligne cohomology
• Twisted Morava K-theory and connective covers of Lie groups
• Parametrized geometric cobordism and smooth Thom stacks
• Noncommutative Differential K-theory