On the coarse classification of tight contact structures

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

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

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

Vincent Colin, Emmanuel Giroux, Ko Honda. On the coarse classification of tight contact structures. Topology and geometry of manifolds, 2003, Athens, Georgia, United States. ⟨hal-00009385⟩