Finitude homotopique et isotopique des structures de contact tendues

Vincent Colin (1) , Emmanuel Giroux (2) , Ko Honda (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 Department of Mathematics

Let V be a closed 3-manifold. In this paper we prove that the homotopy classes of plane fields on V that contain tight contact structures are in finite number and that, if V is atoroidal, the isotopy classes of tight contact structures are also in finite number.

Mots clés: structure de contact tendue; champ de plans; homotopie; isotopie; conjugaison; triangulation; surface branchée

Domaines: Géométrie symplectique [math.SG]; Topologie géométrique [math.GT]

Vincent Colin, Emmanuel Giroux, Ko Honda. Finitude homotopique et isotopique des structures de contact tendues. Publications Mathématiques de L'IHÉS, 2009, 109, pp.245-293. ⟨hal-00280916⟩