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Article Dans Une Revue Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society Année : 2012

Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3

Résumé

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence.
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Dates et versions

hal-00614589 , version 1 (12-08-2011)

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Francois Laudenbach, Gael Gael Meigniez. Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, 2012, 43 (3), pp.347-373. ⟨hal-00614589⟩
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