The minimum dilatation of pseudo-Anosov 5-braids

Ji-Young Ham; Won Taek Song

The minimum dilatation of pseudo-Anosov 5-braids

Geometric Topology 2007-05-23 v3 Dynamical Systems

Authors: Ji-Young Ham , Won Taek Song

Abstract

The minimum dilatation of pseudo-Anosov 5-braids is shown to be the largest zero $\lambda_5 \approx 1.72208$ of $x^4 - x^3 - x^2 - x + 1$ which is attained by $\sigma_1\sigma_2\sigma_3\sigma_4\sigma_1\sigma_2$ .

Keywords

pseudo-Anosov braid minimum dilatation 5-braid mapping class group

Cite

@article{arxiv.math/0506295,
  title  = {The minimum dilatation of pseudo-Anosov 5-braids},
  author = {Ji-Young Ham and Won Taek Song},
  journal= {arXiv preprint arXiv:math/0506295},
  year   = {2007}
}

Comments

21 pages, 9 figures; a Mathematica script included in the source file as fbrmin.m and fbrmin.ps; one more section is added for describing implementation and some more subsections are added to Introduction

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