Geometry & Topology

Universal circles for quasigeodesic flows

Danny Calegari

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Abstract

We show that if M is a hyperbolic 3–manifold which admits a quasigeodesic flow, then π1(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.

Article information

Source
Geom. Topol., Volume 10, Number 4 (2006), 2271-2298.

Dates
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
https://projecteuclid.org/euclid.gt/1513799803

Digital Object Identifier
doi:10.2140/gt.2006.10.2271

Mathematical Reviews number (MathSciNet)
MR2284058

Zentralblatt MATH identifier
1129.57032

Subjects
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

Keywords
quasigeodesic flows universal circles laminations Thurston norm 3-manifolds

Citation

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


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