# Ideal boundaries of pseudo-Anosov flows and applications to large scale structure of flows and foliations

Algebra/Geometry/Topology Seminar

#### by Sergio Fenley

Institution: Florida State University
Date: Tue 9th March 2010
Time: 2:15 PM
Location: Old Geology Theatre 2

Abstract: We consider the asymptotic structure induced by a pseudo-Anosov flow in the universal cover of the underlying 3-manifold. First we show that the orbit space can be compactified to a closed disc. Then we consider untwisted flows: This means that no closed orbit is freely homotopic to the inverse of another orbit. In this case we use the dynamics of the flow to produce a flow ideal boundary to the universal cover of the manifold. The main result is that the action of the fundamental group G of the manifold on the flow ideal boundary is a uniform convergence group. This implies that G is Gromov hyperbolic and the action of G on the flow ideal sphere is conjugate to the action of G on its Gromov ideal boundary. This implies that untwisted pseudo-Anosov flows are quasigeodesic. This also has consequences for the asymptotic behavior of certain foliations.