JournalscmhVol. 87, No. 2pp. 271–302

Homotopy classes of total foliations

  • Masayuki Asaoka

    Kyoto University, Japan
  • Emmanuel Dufraine

    France
  • Takeo Noda

    Toho University, Chiba, Japan
Homotopy classes of total foliations cover

Abstract

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. 271–302

DOI 10.4171/CMH/254