Structure of leaves and the complex Kupka-Smale property

[Structure de feuilles et propriété de Kupka-Smale complexe]

Firsova, Tanya

Annales de l'Institut Fourier, Tome 63 (2013), p. 1849-1879 / Harvested from Numdam

Résumé

Nous étudions la topologie des feuilles d’un feuilletage holomorphe singulier de dimension $1$ sur des variétés de Stein. Nous prouvons que pour un feuilletage générique, toutes les feuilles, sauf au plus un nombre dénombrable, sont contractiles, les autres étant topologiquement des cylindres. Nous montrons aussi qu’un feuilletage générique est Kupka-Smale complexe.

Abstract

We study topology of leaves of $1$-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.

Détail

Publié le : 2013-01-01

MR 3186510 | Zbl 1294.37020

DOI : https://doi.org/10.5802/aif.2816
Classification:  37F75,  32M25,  32E10
Mots clés: feuilletages holomorphes, équations différentielle complexes, variétés de Stein, propriété de Kupka-Smale complexe, propriétés génériques

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