Journal of the Mathematical Society of Japan

Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior

Eiko KIN and Mitsuhiko TAKASAWA

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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.

Article information

J. Math. Soc. Japan, Volume 65, Number 2 (2013), 411-446.

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 37B40: Topological entropy

mapping class group pseudo-Anosov dilatation entropy fibered 3-manifold


KIN, Eiko; TAKASAWA, Mitsuhiko. Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior. J. Math. Soc. Japan 65 (2013), no. 2, 411--446. doi:10.2969/jmsj/06520411.

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