Essential laminations and Haken normal form
It is shown that the existence of an essential lamination in a 3-manifold \(M\) with triangulation \(\tau\) implies the existence of an essential lamination which is in normal form with respect to \(\tau\), in the sense that it intersects every 3-simplex of \(\tau\) in discs which in turn intersect each 1-simplex \(\sigma\) of \(\tau\) in at most one point. The analogous result is well-known for incompressible surfaces in 3-manifolds. In contrast to incompressible surfaces, however, it is not known whether essential laminations can be isotoped into normal form. But one still gets the corollary that an essential lamination exists if and only if one is carried by one of a finite, constructible collection of normal branched surfaces.
scientific article; zbMATH DE number 812628