Quasigeodesic PseudoAnosov flows in hyperbolic 3manifolds
Quasigeodesic PseudoAnosov flows in hyperbolic 3manifolds

Sergio Fenley, Princeton University
Fine Hall 314
We obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudoAnosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits are efficient in measuring length up to a bounded multiplicative distortion when lifted to the universal cover. We prove that such flows are quasigeodesic if and only if there is an upper bound, depending only on the flow, to the number of orbits which are freely homotopic to an arbitrary closed orbit of the flow.