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April, 2013 Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior
Eiko KIN, Mitsuhiko TAKASAWA
J. Math. Soc. Japan 65(2): 411-446 (April, 2013). DOI: 10.2969/jmsj/06520411


We denote by $\delta_g$ (resp. $\delta_g^+$), the minimal dilatation for pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) on a closed surface of genus $g$. This paper concerns the pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the Whitehead sister link exterior $W$ by Dehn filling two cusps, where the fillings are on the boundary slopes of fibers of $W$. We give upper bounds of $\delta_g$ for $g \equiv 0,1,5,6,7,9 \pmod{10}$, $\delta_g^+$ for $g \equiv 1,5,7,9 \pmod{10}$. Our bounds improve the previous one given by Hironaka. We note that the monodromies of fibrations on $W$ were also studied by Aaber and Dunfield independently.


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Eiko KIN. Mitsuhiko TAKASAWA. "Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior." J. Math. Soc. Japan 65 (2) 411 - 446, April, 2013.


Published: April, 2013
First available in Project Euclid: 25 April 2013

zbMATH: 1270.57044
MathSciNet: MR3055592
Digital Object Identifier: 10.2969/jmsj/06520411

Primary: 37E30 , 57M27
Secondary: 37B40

Keywords: dilatation , Entropy , fibered 3-manifold , mapping class group , pseudo-Anosov

Rights: Copyright © 2013 Mathematical Society of Japan


Vol.65 • No. 2 • April, 2013
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