Geometry & Topology 10 (2006) 2271–2298

DOI: 10.2140/gt.2006.10.2271

arXiv: math.GT/0406040

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.

Keywords

quasigeodesic flows, universal circles, laminations, Thurston norm, 3-manifolds

Mathematical Subject Classification

Primary: 57R30

Secondary: 37C10, 37D40, 53C23, 57M50

References

Forward citations

Publication

Received: 15 June 2004
Revised: 10 September 2006
Accepted: 25 October 2006
Published: 29 November 2006
Proposed: David Gabai
Seconded: Benson Farb, Walter Neumann

Authors