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.
Cite this article
Sérgio R. Fenley, Laminar free hyperbolic 3-manifolds. Comment. Math. Helv. 82 (2007), no. 2, pp. 247–321DOI 10.4171/CMH/92