Quasigeodesic Flows in Hyperbolic Three-Manifolds

Abstract

Any closed, oriented, hyperbolic three-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows are pseudo-Anosov flows which are almost transverse to finite depth foliations in the manifold. The main tool is the use of a sutured manifold hierarchy which has good geometric properties.