Universal circles for quasigeodesic flows

Calegari, Danny¹

¹ Department of Mathematics, California Institute of Technology, Pasadena CA, 91125, USA

Geometry & topology, Tome 10 (2006) no. 4, pp. 2271-2298.

Résumé

We show that if $M$ is a hyperbolic $3$–manifold which admits a quasigeodesic flow, then ${\pi }_1\left(M\right)$ 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.

Détail

DOI : 10.2140/gt.2006.10.2271

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

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