Exactness of locally compact groups

TL;DR

This paper characterizes exactness of locally compact second countable groups through topologically amenable actions, providing a new criterion that resolves an open question in the field.

Contribution

It establishes a new equivalence between group exactness and the existence of a topologically amenable action on a compact space.

Findings

Exactness is equivalent to admitting a topologically amenable action.

Provides a new characterization resolving an open question.

Connects group properties with dynamical actions on compact spaces.

Abstract

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.