Abstract
We show that if is a hyperbolic –manifold which admits a quasigeodesic flow, then 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 –manifold without a quasigeodesic flow, answering a long-standing question of Thurston.
Citation
Danny Calegari. "Universal circles for quasigeodesic flows." Geom. Topol. 10 (4) 2271 - 2298, 2006. https://doi.org/10.2140/gt.2006.10.2271
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