Promoting Essential Laminations

Abstract

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuine laminations. In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopic to the identity.

56 pages, 11 figures; version 3: final version, incorporates referee's suggestions

References in corpus (3)

• Laminations and groups of homeomorphisms of the circle
• Laminar Branched Surfaces in 3-manifolds
• Leafwise smoothing laminations

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• Existence of Taut foliations on Seifert fibered homology 3-spheres
• Geometry of foliations and flows I: Almost transverse pseudo-Anosov flows and asymptotic behavior of foliations