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arXiv · 2106.12073

Noncommutative Differential K-theory

Byungdo Park·Arthur J. Parzygnat·Corbett Redden·Augusto Stoffel
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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.

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Byungdo Park, Arthur J. Parzygnat, Corbett Redden, Augusto Stoffel. 2021-06-22. Noncommutative Differential K-theory. https://doi.org/10.1016/j.geomphys.2021.104446

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