We study topology of leaves of -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.
Nous étudions la topologie des feuilles d’un feuilletage holomorphe singulier de dimension 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.
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
Firsova, Tanya 1
@article{AIF_2013__63_5_1849_0, author = {Firsova, Tanya}, title = {Structure of leaves and the complex {Kupka-Smale} property}, journal = {Annales de l'Institut Fourier}, pages = {1849--1879}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {5}, year = {2013}, doi = {10.5802/aif.2816}, mrnumber = {3186510}, zbl = {1294.37020}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2816/} }
TY - JOUR AU - Firsova, Tanya TI - Structure of leaves and the complex Kupka-Smale property JO - Annales de l'Institut Fourier PY - 2013 SP - 1849 EP - 1879 VL - 63 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2816/ DO - 10.5802/aif.2816 LA - en ID - AIF_2013__63_5_1849_0 ER -
%0 Journal Article %A Firsova, Tanya %T Structure of leaves and the complex Kupka-Smale property %J Annales de l'Institut Fourier %D 2013 %P 1849-1879 %V 63 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2816/ %R 10.5802/aif.2816 %G en %F AIF_2013__63_5_1849_0
Firsova, Tanya. Structure of leaves and the complex Kupka-Smale property. Annales de l'Institut Fourier, Volume 63 (2013) no. 5, pp. 1849-1879. doi : 10.5802/aif.2816. https://aif.centre-mersenne.org/articles/10.5802/aif.2816/
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