Noncommutative Differential K-theory
K-Theory and Homology
2022-01-26 v1 Differential Geometry
Abstract
We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression forms as well as a differential refinement of the smooth Serre--Swan correspondence. Our construction subsumes the differential K-theory of a smooth manifold when the algebra is complex-valued smooth functions. Furthermore, our construction fits into a noncommutative differential cohomology hexagon diagram.
Cite
@article{arxiv.2106.12073,
title = {Noncommutative Differential K-theory},
author = {Byungdo Park and Arthur J. Parzygnat and Corbett Redden and Augusto Stoffel},
journal= {arXiv preprint arXiv:2106.12073},
year = {2022}
}
Comments
65 pages