The Baum-Connes conjecture for countable subgroups of SL(2)

TL;DR

This paper proves that the Baum-Connes assembly map is an isomorphism for finitely generated subgroups of SL(2,C) using finite-dimensional methods, providing an alternative approach to previous results.

Contribution

It introduces a new finite-dimensional approach to establish the Baum-Connes conjecture for these groups, differing from prior methods.

Findings

Baum-Connes assembly map is an isomorphism for finitely generated subgroups of SL(2,C)

Provides an alternative proof using finite-dimensional techniques

Advances understanding of the conjecture for specific linear groups

Abstract

We present an alternative approach to the result of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for finitely generated subgroups of SL(2,C). Using finite-dimensional methods, we show that the Baum-Connes assembly map for such groups is an isomorphism.