Moyennabilit\'e \`a l'infini et exactitude d'un groupo\"ide \'etale

TL;DR

This paper introduces a new concept of amenability at infinity for certain groupoids and investigates the exactness of their associated reduced C*-algebras, contributing to the understanding of their analytical properties.

Contribution

It defines amenability at infinity for locally compact, ta groupoids and examines the conditions for the exactness of their reduced C*-algebras, advancing the theory of groupoid C*-algebras.

Findings

Defined amenability at infinity for ta groupoids

Studied conditions for exactness of reduced C*-algebras

Provided examples illustrating the concepts

Abstract

We give a definition of amenability at infinity for a locally compact, $\sigma$-compact and Hausdorff etale groupoid and we study in some case the exactness of the reduced $C^*$-algebra of a such groupoid.