An extreme boundary of acylindrically hyperbolic groups

Wenyuan Yang

An extreme boundary of acylindrically hyperbolic groups

Group Theory 2026-02-16 v2 Operator Algebras

Authors: Wenyuan Yang

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.

Keywords

acylindrical hyperbolic groups minimal action extremely proximal action topologically free action $C^*$-algebras

Cite

@article{arxiv.2511.16400,
  title  = {An extreme boundary of acylindrically hyperbolic groups},
  author = {Wenyuan Yang},
  journal= {arXiv preprint arXiv:2511.16400},
  year   = {2026}
}

Comments

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

Related papers

View all related →