PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

Abstract

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 $\ge {\lambda }_{min,g}$. We will show how a little-known theorem about digraphs gives some insight into ${\lambda }_{min,g}$.

arXiv commentSubmitted inadvertently. This paper is a duplicate of arXiv:1101.2383

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