Commentarii Mathematici Helvetici

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Volume 87, Issue 2, 2012, pp. 271–302
DOI: 10.4171/CMH/254

Published online: 2012-04-17

Homotopy classes of total foliations

Masayuki Asaoka[1], Emmanuel Dufraine[2] and Takeo Noda[3]

(1) Kyoto University, Japan
(2) France
(3) Toho University, Chiba, Japan

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.

Keywords: Foliations, bi-contact structures

Asaoka Masayuki, Dufraine Emmanuel, Noda Takeo: Homotopy classes of total foliations. Comment. Math. Helv. 87 (2012), 271-302. doi: 10.4171/CMH/254