Homotopy classes of total foliations and bi-contact structures on three-manifolds
arXiv:0706.1879
Abstract
On every compact and orientable three-manifold, we construct total foliations (three codimension 1 foliations that are transverse at every point). This construction can be performed on any homotopy class of plane fields with vanishing Euler class. As a corollary we obtain similar results on bi-contact structures.
27 pages, 13 figures. This is the final version. To appear in Comm. Math. Helv