On every compact and orientable three-manifold we construct total foliations (three codimension-one 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.
Cite this article
Masayuki Asaoka, Emmanuel Dufraine, Takeo Noda, Homotopy classes of total foliations. Comment. Math. Helv. 87 (2012), no. 2, pp. 271–302DOI 10.4171/CMH/254