Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Acylindrical hyperbolicity of cubical small cancellation groups

### Goulnara N Arzhantseva and Mark F Hagen

Algebraic & Geometric Topology 22 (2022) 2007–2078
##### 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.

##### Keywords
cubical small-cancellation, acylindrically hyperbolic group, WPD element, contact graph, disc diagram
##### Mathematical Subject Classification 2010
Primary: 20F06, 20F65, 20F67