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Pré-Publication, Document De Travail Année : 2009

Regularization of Gamma_1-structures in dimension 3

Résumé

For co-orientable $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using the perfectness of the group of diffeomorphisms of the circle, nor Mather's homology equivalence. In particular it applies in classes of regularity where perfectness does not hold (or is not known to hold). Moreover the resulting foliation can be chosen of a precise kind, namely an ``open book foliation modified by suspension''.
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Dates et versions

hal-00393726 , version 1 (09-06-2009)
hal-00393726 , version 2 (02-07-2009)
hal-00393726 , version 3 (14-09-2009)

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Francois Laudenbach, Gaël Meigniez. Regularization of Gamma_1-structures in dimension 3. 2009. ⟨hal-00393726v2⟩

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