PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

Details PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials

2011-04-14

arxiv.org/abs/1104.2873v2

Mathematics

Geometric Topology

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

Scientific paper

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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