Primary operations in differential cohomology
Algebraic Topology
2023-09-11 v4 Mathematical Physics
Differential Geometry
math.MP
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 K\"unneth decomposition, that should also be useful in their own right, and point to applications to higher geometry and mathematical physics.
Cite
@article{arxiv.1604.05988,
title = {Primary operations in differential cohomology},
author = {Daniel Grady and Hisham Sati},
journal= {arXiv preprint arXiv:1604.05988},
year = {2023}
}
Comments
36 pages; corrections made to the statement and proof of the K\"unneth formula