A description of the assembly map for the Baum-Connes conjecture with coefficients

TL;DR

This paper develops a configuration space model for equivariant connective K-homology with coefficients in C*-algebras for proper actions, and constructs a connective assembly map that recovers the analytic assembly map.

Contribution

It introduces a new configuration space framework for equivariant K-homology with coefficients and defines a connective assembly map linking to the analytic version.

Findings

Established a configuration space description for equivariant connective K-homology

Defined a connective assembly map that recovers the analytic assembly map

Provided a new perspective on the Baum-Connes assembly process

Abstract

In this note we set a configuration space description of the equivariant connective K-homology groups with coefficients in a unital C*-algebra for proper actions. Over this model we define a connective assembly map and prove that in this setting is possible to recover the analytic assembly map.