Full laminations in 3-manifolds

Abstract

Essential laminations in 3-manifolds, introduced in [GO], are a natural generalization of both incompressible surfaces and foliations without Reeb components. One of the main reasons why essential laminations are of particular interest is that many manifolds which contain no incompressible surfaces contain essential laminations. Indeed, there is some evidence that almost all irreducible manifolds with infinite fundamental group contain essential laminations [B1;D;GM;GO;H;N;R], the only known exceptions being Seifert manifolds [B2]. So essential laminations are potentially a quite powerful tool for studying non-Haken 3-manifolds.