Restriction maps in equivariant $KK$-theory

Abstract

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 $G$-$C^{\ast }$-algebras. Suppose that $K{K}_n^H(A,B)$ is a finitely generated $R(G)$-module for every $H\le G$ closed and $n\in \mathbb{Z}$. Then, if $K{K}_{\ast }^F(A,B)=0$ for all $F\le G$ {\em finite cyclic}, then $K{K}_{\ast }^G(A,B)=0$.

7 pages

References in corpus (1)

• Localization techniques in circle-equivariant KK-theory

Cited by in corpus (2)

• Equivariant Topological T-Duality
• A categorical perspective on the Atiyah-Segal completion theorem in $\mathrm{KK}$-theory