### 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 Σ_{g} of genus g is achieved by the monodromy of some Σ_{g}-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 Σ_{g} 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 Σ_{g}, then where δ(D_{n}) 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 δ_{1,n} is the minimal dilatation of pseudo-Anosovs on a genus 1 surface with n punctures, then.

Original language | English |
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Pages (from-to) | 3537-3602 |

Number of pages | 66 |

Journal | Algebraic and Geometric Topology |

Volume | 13 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2013 Oct 10 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Algebraic and Geometric Topology*,

*13*(6), 3537-3602. https://doi.org/10.2140/agt.2013.13.3537