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A recipe for short-word pseudo-Anosovs
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 4, August 2013
- pp. 1087-1116
- 10.1353/ajm.2013.0037
- Article
- Additional Information
Given any generating set of any subgroup $G$ of the mapping class group of a surface, we find an element $f$ with word length bounded by a constant $K$ depending only on the surface, and with the property that the minimal subsurface supporting a power of $f$ is as large as possible for elements of $G$. In particular, if $G$ contains a pseudo-Anosov map, we find one of word length at most $K$. We also find new examples of convex cocompact free subgroups of the mapping class group.