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Commentarii Mathematici Helvetici

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Volume 82, Issue 2, 2007, pp. 247–321
DOI: 10.4171/CMH/92

Published online: 2007-06-30

Laminar free hyperbolic 3-manifolds

Sérgio R. Fenley[1]

(1) Florida State University, Tallahassee, USA

The purpose of the article is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. The manifolds are obtained by Dehn surgery on torus bundles over the circle. This gives a definitive negative answer to a fundamental question posed by Gabai and Oertel when they introduced essential laminations. The proof is obtained by analysing group actions on on trees and showing that certain 3-manifold groups only have trivial actions on trees. There are corollaries concerning the existence of Reebless foliations and pseudo-Anosov flows.

Keywords: Essential laminations, foliations, pseudo-Anosov flows, hyperbolic 3-manifolds, Dehn surgery, bundles over the torus

Fenley Sérgio R.: Laminar free hyperbolic 3-manifolds. Comment. Math. Helv. 82 (2007), 247-321. doi: 10.4171/CMH/92