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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Universal circles for quasigeodesic flows

Danny Calegari

Geometry & Topology 10 (2006) 2271–2298

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 2000
Primary: 57R30
Secondary: 37C10, 37D40, 53C23, 57M50
References
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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
Danny Calegari
Department of Mathematics
California Institute of Technology
Pasadena CA, 91125
USA