Algebraic K-theory of Fredholm modules and KK-theory

Mathematics – K-Theory and Homology

Scientific paper

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to be published in "Journal of Homotopy and Related Structures"

Scientific paper

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 $\sigma$-unital trivially graded real or complex $C^*$-algebra
acted upon by a fixed compact metrizable group.

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