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

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.

preprint2016arXivOpen access
Hieu Trung DoThomas A. Schmidt
math.DSmath.GT
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Hieu Trung DoThomas A. Schmidt

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