A dynamical characterization of acylindrically hyperbolic groups

TL;DR

This paper provides a dynamical framework to characterize acylindrically hyperbolic groups and demonstrates that non-elementary convergence groups fall into this category, expanding understanding of their structure.

Contribution

It introduces a dynamical characterization of acylindrically hyperbolic groups and links non-elementary convergence groups to this class for the first time.

Findings

Non-elementary convergence groups are acylindrically hyperbolic.

A new dynamical characterization of acylindrically hyperbolic groups is established.

The work broadens the class of groups understood through dynamical properties.

Abstract

We give a dynamical characterization of acylindrically hyperbolic groups. As an application, we prove that non-elementary convergence groups are acylindrically hyperbolic.