Uniformly bounded representations and exact groups

TL;DR

This paper characterizes exact groups by their ability to be approximated through uniformly bounded representations, linking group properties with representation theory.

Contribution

It introduces a new characterization of exact groups using uniformly bounded representations that approximate the trivial representation.

Findings

Exact groups can be characterized by uniformly bounded representations.

The existence of such representations is equivalent to property A.

Provides a new perspective on the structure of exact groups.

Abstract

We characterize groups with Guoliang Yu's property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.