Uniform hyperbolicity of nonseparating curve graphs of nonorientable surfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866929220576346112 |
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| author | Kuno, Erika |
| author_facet | Kuno, Erika |
| contents | Let $N$ be a connected finite type nonorientable surface with or without boundary components and punctures. We prove that the graph of nonseparating curves of $N$ is connected and Gromov hyperbolic with a constant which does not depend on the topological type of the surface by using the bicorn curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs of nonseparating curves for finite type orientable surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_08452 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Uniform hyperbolicity of nonseparating curve graphs of nonorientable surfaces Kuno, Erika Geometric Topology 20F65, 05C25, 57K20 Let $N$ be a connected finite type nonorientable surface with or without boundary components and punctures. We prove that the graph of nonseparating curves of $N$ is connected and Gromov hyperbolic with a constant which does not depend on the topological type of the surface by using the bicorn curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs of nonseparating curves for finite type orientable surfaces. |
| title | Uniform hyperbolicity of nonseparating curve graphs of nonorientable surfaces |
| topic | Geometric Topology 20F65, 05C25, 57K20 |
| url | https://arxiv.org/abs/2108.08452 |