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

2008/12/25 by Eiko Kin, Kin, Eiko, Mitsuhiko Takasawa +1
Mathematics · #37E30 #57M27 (Primary) 57M50 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:37E30 #msc:57M27 #msc:57M50

paper · pdf · doi:10.48550/arxiv.0812.4589

56pages, 22 fugures

arxiv created 2010/06/15 · arxiv updated 2010/06/16

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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