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arXiv · 2508.03477

Computing the $K$-homology $K$-theory product in splitexact algebraic $KK$-theory

Bernhard Burgstaller
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Abstract

Explicit formulas are indicated that compute the product $z \cdot w$ of a level-one element $z \in KK^G(A,{\bf C})$ and any element $w \in KK^G({\bf C},B)$ in splitexact algebraic $KK^G$-theory, or $KK^G$-theory for $C^*$-algebras, with very special $G$-actions. We also make such products accessible to linear-split half-exact $kk$-theory by verifying the existence of a functor from algebraic splitexact $KK$-theory to $kk$-theory.

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Bernhard Burgstaller. 2025-08-05. Computing the $K$-homology $K$-theory product in splitexact algebraic $KK$-theory. https://arxiv.org/abs/2508.03477

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