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arXiv · 2402.15369

Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps

Erwan Lanneau·Livio Liechti·Chi Cheuk Tsang
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Abstract

We show that the stretch factor $λ(f)$ of an orientation-reversing fully-punctured pseudo-Anosov map $f$ on a finite-type orientable surface $S$, with $-χ(S) \geq 4$ and having at least two puncture orbits, satisfies the inequality $λ(f)^{-χ(S)} \geq σ^2$, where $σ=1+\sqrt{2}$ is the silver ratio. We provide examples showing that this bound is asymptotically sharp. This extends previous results of Hironaka and the third author to orientation-reversing maps.

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Erwan Lanneau, Livio Liechti, Chi Cheuk Tsang. 2024-10-21. Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps. https://doi.org/10.1090/tran%2F9350

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