Paires de structures de contact sur les variétés de dimension trois

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

2008-01-07

arxiv.org/abs/0801.1026v2

Mathematics

Symplectic Geometry

21 pages, we correct several mistakes of v1

Scientific paper

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 "\`a la Reeb" for positive pairs of tight contact structures.

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