Geometry & Topology
- Geom. Topol.
- Volume 10, Number 4 (2006), 2271-2298.
Universal circles for quasigeodesic flows
We show that if is a hyperbolic –manifold which admits a quasigeodesic flow, then 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 –manifold without a quasigeodesic flow, answering a long-standing question of Thurston.
Geom. Topol., Volume 10, Number 4 (2006), 2271-2298.
Received: 15 June 2004
Revised: 10 September 2006
Accepted: 25 October 2006
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R30: Foliations; geometric theory
Secondary: 37C10: Vector fields, flows, ordinary differential equations 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 57M50: Geometric structures on low-dimensional manifolds
Calegari, Danny. Universal circles for quasigeodesic flows. Geom. Topol. 10 (2006), no. 4, 2271--2298. doi:10.2140/gt.2006.10.2271. https://projecteuclid.org/euclid.gt/1513799803