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Low dilatation pseudo-Anosovs on punctured surfaces and volume.

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Abstract

For a pseudo-Anosov homeomorphism f on a closed surface of genus \(g\ge 2\), 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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  1. Nanjing University of Science and Technology, Jiangyin, China

    Shixuan Li

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Li, S. Low dilatation pseudo-Anosovs on punctured surfaces and volume.. Geom Dedicata 218, 23 (2024). https://doi.org/10.1007/s10711-023-00860-5

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