Minimum dilatations of pseudo-Anosov braids

Chi Cheuk Tsang; Xiangzhuo Zeng

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arXiv · 2412.01648

Minimum dilatations of pseudo-Anosov braids

Chi Cheuk Tsang·Xiangzhuo Zeng

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Abstract

We determine the minimum dilatation $\delta_n$ 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 $\lim_{n \to \infty} \delta_n^n = (2+\sqrt{3})^2 \approx 13.928$. 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 $n$.

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BibTeX RIS

Chi Cheuk Tsang, Xiangzhuo Zeng. 2024-12-02. Minimum dilatations of pseudo-Anosov braids. https://arxiv.org/abs/2412.01648

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