Regularity of quasigeodesics characterises hyperbolicity
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912319764692992 |
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| author | Hughes, Sam Nairne, Patrick S. Spriano, Davide |
| author_facet | Hughes, Sam Nairne, Patrick S. Spriano, Davide |
| contents | We characterise hyperbolic groups in terms of quasigeodesics in the Cayley graph forming regular languages. We also obtain a quantitative characterisation of hyperbolicity of geodesic metric spaces by the non-existence of certain local (3,0)-quasigeodesic loops. As an application we make progress towards a question of Shapiro regarding groups admitting a uniquely geodesic Cayley graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08573 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Regularity of quasigeodesics characterises hyperbolicity Hughes, Sam Nairne, Patrick S. Spriano, Davide Group Theory 20F67, 68Q45 We characterise hyperbolic groups in terms of quasigeodesics in the Cayley graph forming regular languages. We also obtain a quantitative characterisation of hyperbolicity of geodesic metric spaces by the non-existence of certain local (3,0)-quasigeodesic loops. As an application we make progress towards a question of Shapiro regarding groups admitting a uniquely geodesic Cayley graph. |
| title | Regularity of quasigeodesics characterises hyperbolicity |
| topic | Group Theory 20F67, 68Q45 |
| url | https://arxiv.org/abs/2205.08573 |