Universal circles for quasigeodesic flows

Details Universal circles for quasigeodesic flows Universal circles for quasigeodesic flows

2004-06-02

arxiv.org/abs/math/0406040v4

Geom. Topol. 10 (2006) 2271-2298

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 29 November 2006. V4: typsetting corrections

Scientific paper

10.2140/gt.2006.10.2271

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.

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