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Acylindrical hyperbolicity of cubical small cancellation groups

Goulnara N Arzhantseva and Mark F Hagen

Algebraic & Geometric Topology 22 (2022) 2007–2078

We provide an analogue of Strebel’s classification of geodesic triangles in classical C(1 6) 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.

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cubical small-cancellation, acylindrically hyperbolic group, WPD element, contact graph, disc diagram
Mathematical Subject Classification 2010
Primary: 20F06, 20F65, 20F67
Received: 7 December 2018
Revised: 7 March 2021
Accepted: 6 April 2021
Published: 25 October 2022
Goulnara N Arzhantseva
Faculty of Mathematics
University of Vienna
Mark F Hagen
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
United Kingdom
School of Mathematics
University of Bristol
United Kingdom