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arXiv · 2304.12607

KK- and E-theory via homotopy theory

Ulrich Bunke
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Abstract

We provide a homotopy theorist's point of view on $KK$- and $E$-theory for $C^{*}$-algebras. We construct stable $\infty$-categories representing these theories through a sequence of Dwyer-Kan localizations of the category of $C^{*}$-algebras. Thereby we will reveal the homotopic theoretic meaning of various classical construction from $C^{*}$-algebra theory, in particular of Cuntz' $q$-construction. We will also discuss operator algebra $K$-theory in this framework.

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Ulrich Bunke. 2023-04-25. KK- and E-theory via homotopy theory. https://doi.org/10.2140/om.2024.1.103

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