On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus

By Erwan Lanneau, Jean-Luc Thiffeault. 2009

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We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham's proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus g=2 to 5, the mimimum dilatation is the smallest Salem number for polynomials of degree 2g.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

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