Homotopy classes of total foliations and bi-contact structures on three-manifolds

Masayuki Asaoka; Emmanuel Dufraine; Takeo Noda

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arXiv · 0706.1879

Homotopy classes of total foliations and bi-contact structures on three-manifolds

Masayuki Asaoka·Emmanuel Dufraine·Takeo Noda

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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.

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Masayuki Asaoka, Emmanuel Dufraine, Takeo Noda. 2009-10-19. Homotopy classes of total foliations and bi-contact structures on three-manifolds. https://arxiv.org/abs/0706.1879

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