TY - JOUR

T1 - Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior

AU - Kin, Eiko

AU - Kojima, Sadayoshi

AU - Takasawa, Mitsuhiko

PY - 2013/10/10

Y1 - 2013/10/10

N2 - This paper concerns the set M̂ of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the magic 3-manifold N by Dehn filling three cusps with a mild restriction. Let N(r) be the manifold obtained from N by Dehn filling one cusp along the slope r ∈ ℚ. We prove that for each g (resp. g ≢(mod 6)), the minimum among dilatations of elements (resp. elements with orientable invariant foliations) of M̂ defined on a closed surface Σg of genus g is achieved by the monodromy of some Σg-bundle over the circle obtained from N(3/-2) or N(1/-2) by Dehn filling both cusps. These minimizers are the same ones identified by Hironaka, Aaber and Dunfield, Kin and Takasawa independently. In the case g ≡ (mod 12) we find a new family of pseudo-Anosovs defined on Σg with orientable invariant foliations obtained from N(-6) or N(4) by Dehn filling both cusps. We prove that if δ+g is the minimal dilatation of pseudo-Anosovs with orientable invariant foliations defined on Σg, then where δ(Dn) is the minimal dilatation of pseudo-Anosovs on an n-punctured disk. We also study monodromies of fibrations on N(1). We prove that if δ1,n is the minimal dilatation of pseudo-Anosovs on a genus 1 surface with n punctures, then.

AB - This paper concerns the set M̂ of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the magic 3-manifold N by Dehn filling three cusps with a mild restriction. Let N(r) be the manifold obtained from N by Dehn filling one cusp along the slope r ∈ ℚ. We prove that for each g (resp. g ≢(mod 6)), the minimum among dilatations of elements (resp. elements with orientable invariant foliations) of M̂ defined on a closed surface Σg of genus g is achieved by the monodromy of some Σg-bundle over the circle obtained from N(3/-2) or N(1/-2) by Dehn filling both cusps. These minimizers are the same ones identified by Hironaka, Aaber and Dunfield, Kin and Takasawa independently. In the case g ≡ (mod 12) we find a new family of pseudo-Anosovs defined on Σg with orientable invariant foliations obtained from N(-6) or N(4) by Dehn filling both cusps. We prove that if δ+g is the minimal dilatation of pseudo-Anosovs with orientable invariant foliations defined on Σg, then where δ(Dn) is the minimal dilatation of pseudo-Anosovs on an n-punctured disk. We also study monodromies of fibrations on N(1). We prove that if δ1,n is the minimal dilatation of pseudo-Anosovs on a genus 1 surface with n punctures, then.

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U2 - 10.2140/agt.2013.13.3537

DO - 10.2140/agt.2013.13.3537

M3 - Article

AN - SCOPUS:84885800721

VL - 13

SP - 3537

EP - 3602

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 6

ER -