An extreme boundary of acylindrically hyperbolic groups

Abstract

We prove that every acylindrically hyperbolic group admits a minimal and extremely proximal action on a compact metrizable space. If there are no nontrivial finite normal subgroups, then the action is topologically free. This answers positively a question of Ozawa and the applications to $C^{\ast }$-algebras are discussed.

arXiv comment19 pages, 1 figure; Exposition improved, references updated, Figure 1 and Remark 3.10 added