Mathematics – Geometric Topology
Scientific paper
2010-08-12
Mathematics
Geometric Topology
24 pages, 5 figures
Scientific paper
Given any generating set of any pseudo-Anosov-containing subgroup of the mapping class group of a surface, we construct a pseudo-Anosov with word length bounded by a constant depending only on the surface. More generally, in any subgroup G we find an element f with the property that the minimal subsurface supporting a power of f is as large as possible for elements of G; the same constant bounds the word length of f. Along the way we find new examples of convex cocompact free subgroups of the mapping class group.
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