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Universal circles for quasigeodesic flows

Calegari, Danny (2006) Universal circles for quasigeodesic flows. Geometry and Topology, 10 . pp. 2271-2298. ISSN 1465-3060.

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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.

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Additional Information:© Copyright 2006 Geometry & Topology. Received: 15 June 2004. Revised: 10 September 2006. Accepted: 25 October 2006. Published: 29 November 2006. Proposed: David Gabai. Seconded: Benson Farb, Walter Neumann. I would like to thank Nathan Dunfield for a number of valuable comments and corrections. I would especially like to thank Lee Mosher for bringing my attention to some important references, and for making many detailed and constructive comments and corrections. While this research was carried out, I was partially supported by the Sloan foundation.
Subject Keywords:quasigeodesic flows, universal circles, laminations, Thurston norm, 3-manifolds
Record Number:CaltechAUTHORS:CALgt06c
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7294
Deposited By: Archive Administrator
Deposited On:26 Jan 2007
Last Modified:02 Oct 2019 23:40

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