Acylindrical hyperbolicity of cubical small-cancellation groups

Abstract

We provide an analogue of Strebel's classification of geodesic triangles in classical $C^{\prime }(\frac{1}{6})$ 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.

Revised according to referee comments. This version accepted in Algebraic and Geometric Topology

References in corpus (6)

• On hierarchical hyperbolicity of cubical groups
• A hyperbolic Out(F_n)-complex
• Graphical small cancellation groups with the Haagerup property
• On acylindrical hyperbolicity of groups with positive first ${\ell }^2$-Betti number
• Acylindrical group actions on quasi-trees
• Geometry of infinitely presented small cancellation groups, Rapid Decay and quasi-homomorphisms