An example of a non-amenable dynamical system which is boundary amenable

TL;DR

This paper demonstrates that the action of SL(3,Z) on a specific boundary is amenable, confirming a prediction and providing an example of a non-amenable dynamical system with boundary amenability.

Contribution

It provides the first known example of a non-amenable dynamical system that is boundary amenable, confirming a theoretical prediction.

Findings

SL(3,Z) action on the Stone-Cech boundary is amenable

Confirms Bekka and Kalantar's prediction

Provides a counterexample in dynamical systems

Abstract

It is shown that the action of ${\rm SL}(3,\mathbb{Z})$ on the Stone-\u{C}ech boundary of ${\rm SL}(3,\mathbb{Z}) / {\rm SL}(2,\mathbb{Z}) $ is amenable. This confirms a prediction by Bekka and Kalantar.