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arXiv · 1603.01665

New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant

Hieu Trung Do·Thomas A. Schmidt
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Abstract

We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particular, we give new infinite families of such maps in genus 3.

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Hieu Trung Do, Thomas A. Schmidt. 2016-03-05. New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant. https://arxiv.org/abs/1603.01665

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