  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.
