Strictly systolic angled complexes and hyperbolicity of one-relator groups
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 negat...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2022 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/214851 |
| Acesso em linha: | http://hdl.handle.net/11336/214851 |
| Access Level: | Acceso aberto |
| Palavra-chave: | HYPERBOLICITY SYSTOLICITY ANGLES ONERELATORS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | 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 ) . |
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