2/4/2010

Sergio Fenley
Princeton University

Quasigeodesic pseudo-Anosov flows

A quasigeodesic is a curve which is uniformly efficient in measuring distance in relative homotopy classes or equivalently efficient up to a bounded multiplicative distortion in measuring distance when lifted to the universal cover. A flow is quasigeodesic if all flow lines are quasigeodesics. The talk will explore quasigeodesic pseudo-Anosov flows in atoroidal 3-manifolds, of which there are several infinite families of examples. By geometrization and irreducibility the manifolds are hyperbolic. In such manifolds quasigeodesics are extremely important as for instance they are a bounded distance from minimal geodesics (in the universal cover). One important result is that such flows induce ideal maps from the ideal boundary of the stable/unstable leaves to the boundary of hyperbolic 3-space. The talk will also explore properties of these maps and in particular identification of ideal points. This is connected with the property of the stable/unstable foliations being quasi-isometric foliations. The tools are the dynamics of the flow and also the large scale geometry of the universal cover.