Stable cylinders and fine structures for hyperbolic groups and curve graphs
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| Format: | Preprint |
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2025
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| _version_ | 1866916579564847104 |
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| author | Petyt, Harry Spriano, Davide Zalloum, Abdul |
| author_facet | Petyt, Harry Spriano, Davide Zalloum, Abdul |
| contents | In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve graphs of finite-type surfaces. These cylinders are fine objects, and the core of our approach is to upgrade the hyperbolic space to one with improved fine properties via a generalisation of Sageev's construction. The methods also let us prove that curve graphs of surfaces admit equivariant quasiisometric embeddings in finite products of quasitrees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable cylinders and fine structures for hyperbolic groups and curve graphs Petyt, Harry Spriano, Davide Zalloum, Abdul Geometric Topology Group Theory Metric Geometry In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve graphs of finite-type surfaces. These cylinders are fine objects, and the core of our approach is to upgrade the hyperbolic space to one with improved fine properties via a generalisation of Sageev's construction. The methods also let us prove that curve graphs of surfaces admit equivariant quasiisometric embeddings in finite products of quasitrees. |
| title | Stable cylinders and fine structures for hyperbolic groups and curve graphs |
| topic | Geometric Topology Group Theory Metric Geometry |
| url | https://arxiv.org/abs/2501.13600 |