Acylindrical hyperbolicity of cubical small cancellation groups

Abstract

We provide an analogue of Strebel’s classification of geodesic triangles in classical $C^{\prime }\left(\frac{1}{6}\right)$ groups for groups given by Wise’s cubical presentations satisfying sufficiently strong metric cubical small cancellation conditions. Using our classification, we give conditions guaranteeing that a cubical small cancellation group is acylindrically hyperbolic.