Algebraic degrees of stretch factors in mapping class groups

Hyunshik Shin

Published 2014-01-08, updated 2015-09-23Version 2

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 $d \leq g$.