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

Abstract

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.