Strictly systolic angled complexes and hyperbolicity of one-relator groups

Blufstein, Martín Axel; Minian, Elías

doi:10.2140/agt.2022.22.1159

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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

DOI: 10.2140/agt.2022.22.1159

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 $C^{'} (\frac{1}{6})$ and $C^{'} (\frac{1}{4}) - T (4)$ .

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

Volume 22, issue 3 (2022)