Regularization of Gamma_1-structures in dimension 3

Francois Laudenbach (1) , Gaël Meigniez (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting foliation can be chosen of a precise kind, namely an ''open book foliation modified by suspension''. There is also a model in the non co-orientable case.

Mots clés: Foliations; Haefliger's Gamma-structures; open book

Domaines: Topologie géométrique [math.GT]

Francois Laudenbach, Gaël Meigniez. Regularization of Gamma_1-structures in dimension 3. 2009. ⟨hal-00393726v3⟩