Algebraic degrees of stretch factors in mapping class groups

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 $d\le g$.

19 pages, 5 figures; The revision contains new proof by Coxeter theory as suggested by the referee. Final version. To appear in AGT

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