La conjecture de Baum-Connes \`a coefficients pour les groupes hyperboliques

TL;DR

This paper proves the Baum-Connes conjecture with coefficients for hyperbolic groups by establishing the surjectivity of the Baum-Connes map, complementing previous work on its injectivity.

Contribution

The paper completes the proof of the Baum-Connes conjecture with coefficients for hyperbolic groups by demonstrating the surjectivity of the Baum-Connes map.

Findings

Injectivity of the Baum-Connes map was previously established.

This work proves the surjectivity for hyperbolic groups.

The conjecture holds with coefficients for these groups.

Abstract

This paper gives a proof of the Baum-Connes conjecture with coefficients for hyperbolic groups. More precisely the injectivity of the Baum-Connes map was established by Kasparov and Skandalis and we prove the surjectivity.