A localization algebra approach to the Baum-Connes conjecture for extensions

Abstract

For an extension $1\rightarrow N \rightarrow \Gamma \xrightarrow{q} \Gamma / N \rightarrow 1$ of discrete countable groups, it is known that the Baum-Connes conjecture with coefficients holds for $\Gamma$ if it holds for $\Gamma / N$ and $q^{-1}(F)$ for any finite subgroup $F$ of $\Gamma / N$. In this paper, we employ a localization algebra approach to prove this result.