Acylindrical hyperbolicity of cubical small cancellation groups

Arzhantseva, Goulnara N; Hagen, Mark F

doi:10.2140/agt.2022.22.2007

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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

DOI: 10.2140/agt.2022.22.2007

Abstract

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

Keywords

cubical small-cancellation, acylindrically hyperbolic group, WPD element, contact graph, disc diagram

Mathematical Subject Classification 2010

Primary: 20F06, 20F65, 20F67

References

Publication

Received: 7 December 2018

Revised: 7 March 2021

Accepted: 6 April 2021

Published: 25 October 2022

Authors

Goulnara N Arzhantseva
Faculty of Mathematics University of Vienna Vienna Austria

Mark F Hagen
Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom	School of Mathematics University of Bristol Bristol United Kingdom

Volume 22, issue 5 (2022)