Pseudo-Anosov flows and incompressible tori
by
Sergio Fenley
Washington University

Pseudo-Anosov flows are incredibly common amongst 3-manifolds. It is easy to show that a 3-manifold supporting a pseudo-Anosov flow is irreducible. However there are many situations where the manifold is toroidal. Our goal is to understand the relationship of the flow with an embedded incompressible torus and more generally with a subgroup A = Z + Z of the fundamental group. We prove that if no element of A can be represented by a closed orbit of the flow, then the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus - an extremely restrictive situation. In all the other cases the Z + Z can be geometrically represented by a free homotopy from a closed orbit to itself and put in a canonical form. The key tool is an analysis of group actions on non Hausdorff trees, also known as order trees - we produce an invariant axis in the free case. There are applications to the study of R-covered foliations.

Date received: January 31, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagh-28.