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

Abstract

We denote by δ_g (resp. δ_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 δ_g for g ≡ 0,1,5,6,7,9 (mod 10), δ_g⁺ for g ≡ 1,5,7,9 (mod 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.