# Paires de structures de contact sur les variétés de dimension trois

1 LMJL - Laboratoire de Mathématiques Jean Leray 2 Departemento de matematica

Abstract : We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $\lambda$. We prove that if $\lambda$ is uniquely integrable and if both structures of the pair are tight, then the integral foliation of $\lambda$ doesn-t contain any Reeb component whose core curve is homologous to zero. Moreover, the ambient manifold carries a Reebless foliation. We also show a stability theorem -à la Reeb- for positive pairs of tight contact structures.

Mots-clés : paire composante de Reeb feuilletage tendu structure de contact

Author: Vincent Colin - Sebastiao Firmo -

Source: https://hal.archives-ouvertes.fr/