Small dilatations of pseudo-Anosov maps on hyperelliptic translation surfaces

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• Corentin Boissy, Aix-Marseille
• Wednesday 20 October 2010, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

A pseuso-Anosov homeomorhism on a surface naturally defines a pair of transverse measured foliations, and in this way, a flat structure on the surface. If the foliations are oriented, we obtain a translation surface for which the map is affine. In this talk, we will prove that the dilatation of any pseudo-Anosov homeomorphism on a translation surface that belongs to a hyperelliptic component is bounded from below by the square root of 2, independently of the genus. This is in contrast to Penner’s asymptotic: indeed, he proved that the least dilatation of any pseudo-Anosov homeomorphism on a surface of genus g tends to one as g tends to infinity.

This talk is part of the Differential Geometry and Topology Seminar series.

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