#### Volume 22, issue 3 (2022)

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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 ${C}^{\prime }\left(\frac{1}{6}\right)$ and ${C}^{\prime }\left(\frac{1}{4}\right)-T\left(4\right)$.

##### Keywords
hyperbolic groups, one-relator groups, systolic complexes
##### Mathematical Subject Classification 2010
Primary: 20F06, 20F65, 20F67
Secondary: 57M07, 57M20