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arxiv: math/0406040 · v4 · submitted 2004-06-02 · 🧮 math.GT · math.DS

Universal circles for quasigeodesic flows

classification 🧮 math.GT math.DS
keywords quasigeodesiccircleflowflowshyperbolicmanifoldthurstonuniversal
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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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