A recipe for short-word pseudo-Anosovs

Abstract

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.

24 pages, 5 figures

References in corpus (3)

• Subgroup classification in Out(F_n)
• Knots, sutures and excision
• The classification of Kleinian surface groups, I: Models and bounds