Boundary amenability of groups via ultrapowers

TL;DR

This paper introduces a novel approach using C*-algebra ultrapowers to construct the Stone-Cech compactification and proves boundary amenability for groups acting on trees.

Contribution

It provides a new construction method for the Stone-Cech compactification and offers a novel proof of boundary amenability for certain groups.

Findings

New construction of Stone-Cech compactification via ultrapowers

Proof that groups acting on trees are boundary amenable

Application of C*-algebra ultrapowers in topological group theory

Abstract

We use $\mathrm{C}^{\ast}$-algebra ultrapowers to give a new construction of the Stone-Cech compactification of a separable, locally compact space. We use this construction to give a new proof of the fact that groups that act isometrically, properly, and transitively on trees are boundary amenable.