Pseudo-Anosov braids with small entropy and the magic 3-manifold

Eiko Kin; Mitsuhiko Takasawa

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arXiv · 0812.4589

Pseudo-Anosov braids with small entropy and the magic 3-manifold

Eiko Kin·Mitsuhiko Takasawa

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Abstract

We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called "the magic manifold". We compute the entropy function on the fiber face of the unit ball with respect to the Thurston norm, determine homology classes whose representatives are genus 0 fiber surfaces, and describe their monodromies by braids. Among such homology classes whose representatives have n punctures, we decide which one realizes the minimal entropy. It turns out that all the braids with smallest known entropy are derived from monodromies for such homology classes.

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BibTeX RIS

Eiko Kin, Mitsuhiko Takasawa. 2010-06-15. Pseudo-Anosov braids with small entropy and the magic 3-manifold. https://arxiv.org/abs/0812.4589

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