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

Abstract

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.

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

References in corpus (2)

• A family of pseudo-Anosov braids with small dilatation
• Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid

Cited by in corpus (8)

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• The cat's cradle, stirring, and topological complexity
• On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers