The Baum-Connes conjecture, Swan group actions and controlled topology

TL;DR

This paper presents a novel proof for certain cases of the Baum-Connes conjecture by adapting techniques from the proof of the Farrell-Jones conjecture, advancing understanding in geometric topology.

Contribution

It introduces a new proof approach for parts of the Baum-Connes conjecture inspired by Farrell-Jones methods, offering potential for broader applicability.

Findings

New proof for specific cases of the Baum-Connes conjecture

Methodology inspired by Farrell-Jones conjecture proof

Potential implications for controlled topology and group actions

Abstract

We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.