The minimum dilatation of pseudo-Anosov 5-braids

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 ${\sigma }_1{\sigma }_2{\sigma }_3{\sigma }_4{\sigma }_1{\sigma }_2$.

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