Amenable purely infinite actions on the non-compact Cantor set

TL;DR

The paper proves that every countable non-amenable group can act freely, minimally, amenably, and purely infinitely on the non-compact Cantor set, answering a significant open question.

Contribution

It establishes the existence of such complex actions for all countable non-amenable groups, expanding understanding of group actions on topological spaces.

Findings

Existence of free minimal amenable purely infinite actions for all countable non-amenable groups

Answers an open question posed by Kellerhals, Monod, and R{ }ordam

Advances the theory of group actions on the non-compact Cantor set

Abstract

We prove that any countable non-amenable group G admits a free minimal amenable purely infinite action on the non-compact Cantor set. This answers a question of Kellerhals, Monod and R{\o}rdam.