Low dilatation pseudo-Anosovs on punctured surfaces and volume

Shixuan Li

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arXiv · 1912.13299

Low dilatation pseudo-Anosovs on punctured surfaces and volume

Shixuan Li

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Abstract

For a pseudo-Anosov homeomorphism $f$ on a closed surface of genus $g\geq 2$, for which the entropy is on the order $\frac{1}{g}$ (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of $g$. We show that the analogous result fails for a surface of fixed genus $g$ with $n$ punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order $\frac{\log n}{n}$, and volume tending to infinity.

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BibTeX RIS

Shixuan Li. 2019-12-31. Low dilatation pseudo-Anosovs on punctured surfaces and volume. https://arxiv.org/abs/1912.13299

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