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

Eiko Kin, Sadayoshi Kojima, Mitsuhiko Takasawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)3537-3602
Number of pages66
JournalAlgebraic and Geometric Topology
Volume13
Issue number6
DOIs
Publication statusPublished - 2013 Oct 10
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior'. Together they form a unique fingerprint.

  • Cite this