Acylindrical hyperbolicity of cubical small-cancellation groups

TL;DR

This paper classifies geodesic triangles in cubical small-cancellation groups and proves that, under certain conditions, these groups are acylindrically hyperbolic, extending classical results to a cubical setting.

Contribution

It provides a classification of geodesic triangles in cubical small-cancellation groups and establishes acylindrical hyperbolicity for a broad class of these groups.

Findings

Most cubical small-cancellation groups are acylindrically hyperbolic.

The classification extends Strebel's classical results to cubical groups.

Degenerate cases are explicitly characterized.

Abstract

We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small cancellation conditions. Using our classification, we prove that, except in specific degenerate cases, such groups are acylindrically hyperbolic.