Kirchberg--Wassermann exactness vs exactness: reduction to the unimodular totally disconnected case

TL;DR

This paper demonstrates that establishing KW-exactness for all second countable locally compact groups can be reduced to proving it for the subclass of totally disconnected groups, simplifying the overall proof strategy.

Contribution

It reduces the problem of proving KW-exactness for general groups to the case of totally disconnected groups, providing a significant simplification.

Findings

KW-exactness for second countable locally compact groups can be verified by checking totally disconnected groups.

The reduction simplifies the approach to proving exactness properties in group C*-algebras.

The result connects the properties of general groups to those of a specific subclass, aiding future research.

Abstract

We show that in order to prove that every second countable locally compact groups with exact reduced group C*-algebra is exact in the dynamical sense (i.e. KW-exact) it suffices to show this for totally disconnected groups.