Rotation sets and axes in the fine curve graph for torus homeomorphisms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909916536504320 |
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| author | Hensel, Sebastian Roux, Frédéric Le |
| author_facet | Hensel, Sebastian Roux, Frédéric Le |
| contents | We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A key ingredient is a metric version of the classical WPD property from geometric group theory.
As a consequence we find new stable criteria for positive scl, and for two homeomorphisms to generate a free group, and we provide a Tits alternative for groups of torus homeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rotation sets and axes in the fine curve graph for torus homeomorphisms Hensel, Sebastian Roux, Frédéric Le Group Theory Dynamical Systems We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A key ingredient is a metric version of the classical WPD property from geometric group theory. As a consequence we find new stable criteria for positive scl, and for two homeomorphisms to generate a free group, and we provide a Tits alternative for groups of torus homeomorphisms. |
| title | Rotation sets and axes in the fine curve graph for torus homeomorphisms |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2509.26156 |