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arXiv · 2610.17060

A higher categorical approach to graded bivariant $K$-theories for Real $C^*$-algebras

Anupam Datta
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Abstract

We present an $\infty$-categorical refinement of classical $KK$-theory and $E$-theory for graded, $G$-equivariant for a locally compact second countable group $G$, Real $C^*$-algebras. As a consequence, we obtain a couple of fiber sequences connecting the different $K$-theory spectra, and explicitly analyse the induced endomorphisms on $K_0$-groups. We also answer precisely some folklore questions in the area. Among other things, we show that graded $KK$- and $E$-categories are not a Dwyer-Kan localization of graded $C^*$-algebras.

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Anupam Datta. 2026-10-12. A higher categorical approach to graded bivariant $K$-theories for Real $C^*$-algebras. https://arxiv.org/abs/2610.17060

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