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Algebraic K-theory of Fredholm modules and KK-theory

Tamaz Kandelaki
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Abstract

Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic $K$-theory spectrum of the additive category of Fredholm $(A,B)$-bimodules for $A$ and $B$, respectively, a separable and $σ$-unital trivially graded real or complex $C^*$-algebra acted upon by a fixed compact metrizable group.

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Tamaz Kandelaki. 2006-09-07. Algebraic K-theory of Fredholm modules and KK-theory. https://arxiv.org/abs/math/0609208

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