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arXiv · 2210.13418

Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor

Eriko Hironaka·Chi Cheuk Tsang
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Abstract

We show that given a fully-punctured pseudo-Anosov map $f:S \to S$ whose punctures lie in at least two orbits under the action of $f$, the expansion factor $λ(f)$ satisfies the inequality $λ(f)^{|χ(S)|} \ge μ^4 \approx 6.85408$, where $μ= \frac{1 + \sqrt{5}}{2} \approx 1.61803$ is the golden ratio. The proof involves a study of standardly embedded train tracks, and the Thurston symplectic form defined on their weight space.

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Eriko Hironaka, Chi Cheuk Tsang. 2024-01-03. Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor. https://arxiv.org/abs/2210.13418

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