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

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

2009-05-08

arxiv.org/abs/0905.1302v3

Annales de l'Institut Fourier 61 (1), 105-144, 2011

Mathematics

Geometric Topology

30 pages, 6 figures. amsart style. To appear in Annales de l'Institut Fourier. Added one reference in v3.

Scientific paper

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.

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