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2010 Small dilatation mapping classes coming from the simplest hyperbolic braid
Eriko Hironaka
Algebr. Geom. Topol. 10(4): 2041-2060 (2010). DOI: 10.2140/agt.2010.10.2041


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

limsup g ( δ g ) g 3 + 5 2 .


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Eriko Hironaka. "Small dilatation mapping classes coming from the simplest hyperbolic braid." Algebr. Geom. Topol. 10 (4) 2041 - 2060, 2010.


Received: 29 October 2009; Revised: 16 April 2010; Accepted: 10 May 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1221.57028
MathSciNet: MR2728483
Digital Object Identifier: 10.2140/agt.2010.10.2041

Primary: 57M50
Secondary: 57M25

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

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 4 • 2010
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