On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers

Joan S. Birman

Published 2011-01-12, updated 2011-04-14Version 2

It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $\lambda_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has dilatation $\geq \lambda_{min,g}$. We will show how a little-known theorem about digraphs gives some insight into $\lambda_{min,g}$.