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Currently displaying 1 – 2 of 2

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Sur la géométrie des structures de contact invariantes

Robert Lutz — 1979

Annales de l'institut Fourier

À toute structure de contact $σ$ invariante par rapport à une action localement libre d’un groupe de Lie $G_{k}$ sur une variété compacte $M$ , on associe une fibration au-dessus de $S^{k - 1}$ nouée, à la manière des pages d’un livre ouvert, le long de l’ensemble des points où l’orbite de l’action est tangente au plan de $σ$ . Après en avoir déduit des contraintes sur $G$ et $M$ , on construit des structures de contact invariantes nouvelles à partir de fibrations nouées et on en donne des critères de classification équivariante....

Structures de contact sur les fibrés principaux en cercles de dimension trois

Robert Lutz — 1977

Annales de l'institut Fourier

On construit et classifie à conjugaison équivariante près toutes les formes de contact invariantes sur un fibré principal en cercles $M_{3} \to B_{2}$ ( $M$ compact). Si $\tilde{M} = S^{3}$ , les formes obtenues induisent sur $S^{3}$ des formes de contact dans chaque classe d’homotopie de 1-formes sans zéros : on en déduit que $M$ admet une infinité de structures de contact non isomorphes.

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