A geometric criterion to be pseudo-Anosov

Abstract

We establish a criterion for certain mapping classes of a surface homeomorphisms to be pseudo-Anosov in terms of the geometry of hyperbolic 3-manifolds and Gromov-hyperbolic surface group extensions. Specifically, any element of the fundamental group of a surface S gives rise to a mapping class on the punctured surface, and we show that such a class is pseudo-Anosov if its geodesic representative is "wide" in some hyperbolic 3-manifold homeomorphic to the trivial interval bundle over S.

v2. To appear in the Michigan Mathematical Journal. Revised according to referees' comments. 24 pages, no figures. v1. 21 pages, no figures