PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

Joan S. Birman

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arXiv · 1104.2873

PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

Joan S. Birman

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

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Joan S. Birman. 2011-04-14. PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials. https://arxiv.org/abs/1104.2873

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