Minimum dilatations of pseudo-Anosov braids
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918182906757120 |
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| author | Tsang, Chi Cheuk Zeng, Xiangzhuo |
| author_facet | Tsang, Chi Cheuk Zeng, Xiangzhuo |
| contents | We determine the minimum dilatation $δ_n$ among pseudo-Anosov braids with $n$ strands, for large enough values of $n$. These are the dilatations attained by the examples of Hironaka-Kin and Venzke, and they satisfy $\lim_{n \to \infty} δ_n^n = (2+\sqrt{3})^2 \approx 13.928$. Together with previous work, this result confirms conjectures by Kin-Takasawa and Venzke, and solves the minimum dilatation problem on the $n$-punctured sphere, for all but $6$ values of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum dilatations of pseudo-Anosov braids Tsang, Chi Cheuk Zeng, Xiangzhuo Geometric Topology Dynamical Systems We determine the minimum dilatation $δ_n$ among pseudo-Anosov braids with $n$ strands, for large enough values of $n$. These are the dilatations attained by the examples of Hironaka-Kin and Venzke, and they satisfy $\lim_{n \to \infty} δ_n^n = (2+\sqrt{3})^2 \approx 13.928$. Together with previous work, this result confirms conjectures by Kin-Takasawa and Venzke, and solves the minimum dilatation problem on the $n$-punctured sphere, for all but $6$ values of $n$. |
| title | Minimum dilatations of pseudo-Anosov braids |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2412.01648 |