Essential Laminations in 3-Manifolds

Heegaard surfaces and measured laminations, I: The Waldhausen conjecture

“…The proof involves some basic properties of foliations and laminations, such as the Reeb stability theorem and local stability theorem. We refer to [4,5,42] for more details, see also [12] for lamination versions of these results. The Reeb stability theorem basically says that the holonomy along a trivial curve in a leaf must be trivial.…”

“…Note that the C 2 assumption in Novikov's original proof is not necessary, see [40] or section 9.3 of [6]. We will use an adaptation of Novikov's argument as in the proof of Lemma 2.8 of [12]. Our proof is based on the proof of Lemma 2.8 of [12] (pp 54).…”

“…We will use an adaptation of Novikov's argument as in the proof of Lemma 2.8 of [12]. Our proof is based on the proof of Lemma 2.8 of [12] (pp 54). So, before we proceed, we briefly describe the argument in [12], which shows that a lamination fully carried by an essential branched surface has no vanishing cycle.…”

“…Our proof is based on the proof of Lemma 2.8 of [12] (pp 54). So, before we proceed, we briefly describe the argument in [12], which shows that a lamination fully carried by an essential branched surface has no vanishing cycle. In that proof [12], the lamination λ is fully carried by N (B) .…”

Tight Contact Structures on Laminar Free Hyperbolic Three-Manifolds

“…A generalization of taut foliations of 3-manifolds is the notion of an essential lamination introduced by Gabai and Oertel [12]. A lamination is a foliation of a closed subset of the manifold.…”