Small dilatation mapping classes coming from the simplest hyperbolic braid

Hironaka, Eriko¹

¹Department of Mathematics, Florida State University, Tallahasse FL 32301, USA

Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2041-2060

Résumé

In this paper we study the small dilatation pseudo-Anosov mapping classes arising from fibrations over the circle of a single 3–manifold, the mapping torus for the “simplest hyperbolic braid”. The dilatations that occur include the minimum dilatations for orientable pseudo-Anosov mapping classes for genus g = 2,3,4,5 and 8. We obtain the “Lehmer example” in genus g = 5, and Lanneau and Thiffeault’s conjectural minima in the orientable case for all genus g satisfying g = 2 or 4(mod6). Our examples show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when g = 4,6 or 8. We also prove that if δg is the minimum dilatation of pseudo-Anosov mapping classes on a genus g surface, then

Détail

DOI : 10.2140/agt.2010.10.2041

Keywords: Teichmüller polynomial, pseudo-Anosov mapping classes, minimal dilatations

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