Primary operations in differential cohomology
arXiv:1604.05988 · doi:10.1016/j.aim.2018.07.019
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.
36 pages; corrections made to the statement and proof of the Künneth formula
References in corpus (3)
Cited by in corpus (8)
- The character map in (twisted differential) non-abelian cohomology
- Ramond-Ramond fields and twisted differential K-theory
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- Spectral sequences in smooth generalized cohomology
- Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
- Twisted differential KO-theory
- Differential cohomology (encyclopedia article)
- Parametrized geometric cobordism and smooth Thom stacks