Universal circles for quasigeodesic flows
Geometric Topology
2009-04-22 v4 Dynamical Systems
Abstract
We show that if M is a hyperbolic 3-manifold which admits a quasigeodesic flow, then pi_1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that the Thurston norm can be characterized by quasigeodesic flows, thereby generalizing a theorem of Mosher, and we give the first example of a closed hyperbolic 3-manifold without a quasigeodesic flow, answering a long-standing question of Thurston.
Cite
@article{arxiv.math/0406040,
title = {Universal circles for quasigeodesic flows},
author = {Danny Calegari},
journal= {arXiv preprint arXiv:math/0406040},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 29 November 2006. V4: typsetting corrections