Abstract
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 and . We obtain the “Lehmer example” in genus , and Lanneau and Thiffeault’s conjectural minima in the orientable case for all genus satisfying or . Our examples show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when or . We also prove that if is the minimum dilatation of pseudo-Anosov mapping classes on a genus surface, then
Citation
Eriko Hironaka. "Small dilatation mapping classes coming from the simplest hyperbolic braid." Algebr. Geom. Topol. 10 (4) 2041 - 2060, 2010. https://doi.org/10.2140/agt.2010.10.2041
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