Restriction maps in equivariant $KK$-theory

Details Restriction maps in equivariant $KK$-theory Restriction maps in equivariant $KK$-theory

2011-01-10

arxiv.org/abs/1101.1859v1

Journal of K-theory, 9 (2012), pp. 45 - 55

Mathematics

K-Theory and Homology

7 pages

Scientific paper

10.1017/is011010005jkt168

We extend McClure's results on the restriction maps in equivariant $K$-theory to bivariant $K$-theory: Let $G$ be a compact Lie group and $A$ and $B$ be $G$-$C^*$-algebras. Suppose that $KK^{H}_{n}(A, B)$ is a finitely generated $R(G)$-module for every $H \le G$ closed and $n \in \Z$. Then, if $KK^{F}_{*}(A, B) = 0$ for all $F \le G$ {\em finite cyclic}, then $KK^{G}_{*}(A, B) = 0$.

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