The minimum dilatation of pseudo-Anosov 5-braids

Ji-Young Ham, Won Taek Song

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