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Strictly systolic angled complexes and hyperbolicity of one-relator groups

Martín Axel Blufstein and Elías Gabriel Minian

Algebraic & Geometric Topology 22 (2022) 1159–1175
Abstract

We introduce the notion of strictly systolic angled complexes. They generalize Januszkiewicz and Świątkowski’s 7–systolic simplicial complexes and also their metric counterparts, which appear as natural analogues to Huang and Osajda’s metrically systolic simplicial complexes in the context of negative curvature. We prove that strictly systolic angled complexes and the groups that act on them geometrically, together with their finitely presented subgroups, are hyperbolic. We use these complexes to study the geometry of one-relator groups without torsion, and prove hyperbolicity of such groups under a metric small cancellation hypothesis, weaker than C(1 6) and C(1 4) T(4).

Keywords
hyperbolic groups, one-relator groups, systolic complexes
Mathematical Subject Classification 2010
Primary: 20F06, 20F65, 20F67
Secondary: 57M07, 57M20
References
Publication
Received: 15 January 2020
Revised: 10 February 2021
Accepted: 8 June 2021
Published: 25 August 2022
Authors
Martín Axel Blufstein
Departamento de Matemática, FCEyN, UBA
Universidad de Buenos Aires
Buenos Aires
Argentina
Elías Gabriel Minian
Departamento de Matemática, FCEyN, UBA
Universidad de Buenos Aires
Buenos Aires
Argentina