Commentarii Mathematici Helvetici
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Volume 87, Issue 2, 2012, pp. 271–302
DOI: 10.4171/CMH/254
Homotopy classes of total foliations
Masayuki Asaoka (1), Emmanuel Dufraine (2) and Takeo Noda (3)
(1) Department of Mathematics, Kyoto University, 606-8502, KYOTO, JAPAN(2) FRANCE
(3) Department of Mathematics, Toho University, 274-8510, 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