Structure of leaves and the complex Kupka-Smale property

Firsova, Tanya

Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1849-1879.

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.

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.

Classification : 37F75, 32M25, 32E10
Keywords: holomorphic foliations, complex differential equations, Stein manifolds, Kupka-Smale property, generic properties
Mot clés : feuilletages holomorphes, équations différentielle complexes, variétés de Stein, propriété de Kupka-Smale complexe, propriétés génériques

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