Characterisation of branched surfaces fully carrying a lamination
Résumé
We give a necessary and sufficient condition for a branched surface in a closed orientable 3-manifold to fully carry a lamination. This answers a problem of D. Gabai : when does a branched surface in a 3-manifold fully carry a lamination? The last part of the text is devoted to contact structures carried by branched surfaces. An application of the result of the previous part is given.