#### Volume 16, issue 3 (2016)

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Algebraic degrees of stretch factors in mapping class groups

### Hyunshik Shin

Algebraic & Geometric Topology 16 (2016) 1567–1584
##### Abstract

We explicitly construct pseudo-Anosov maps on the closed surface of genus $g$ with orientable foliations whose stretch factor $\lambda$ is a Salem number with algebraic degree $2g$. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree $d$, for each positive even integer $d$ such that  $d\le g$.

##### Keywords
pseudo-Anosov, stretch factor, dilatation, algebraic degree, Salem number
##### Mathematical Subject Classification 2010
Primary: 57M50, 57M15