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

Joan S. Birman

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

Geometric Topology 2015-03-17 v2

Authors: Joan S. Birman

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 $\lambda_{min,g}$ .

Keywords

anosov representations diffeomorphism groups mapping class groups of surfaces

Cite

@article{arxiv.1101.2383,
  title  = {On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers},
  author = {Joan S. Birman},
  journal= {arXiv preprint arXiv:1101.2383},
  year   = {2015}
}

Comments

Lemma 3 of version 1 is false. All other changes are minor, and were directed toward making the paper readable without the false lemma. new version has 14 pages, 4 figures

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

Abstract

Keywords

Cite

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