Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincaré domain
[Équivalence topologique des germes de feuilletages holomorphes de rang 1 avec une singularité isolée dans le domaine de Poincaré]
Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 561-590.

Nous démontrons que la classe d’équivalence topologique des germes de feuilletages holomorphiques de rang 1 avec une singularité isolée de type Poincaré est déterminée par la classe d’équivalence topologique du feuilletage réel d’intersection du germe du feuilletage (normalisé) avec une sphère centrée dans la singularité. Nous utilisons ce Theorème de Reconstruction afin de classifier complètement les classes d’équivalence topologique des germes de feuilletages holomorphiques planes de type Poincaré et nous discutons une conjecture sur la classification en dimension 3.

We show that the topological equivalence class of holomorphic foliation germs of rank 1 with an isolated singularity of Poincaré type is determined by the topological equivalence class of the real intersection foliation of the (suitably normalized) foliation germ with a sphere centered in the singularity. We use this Reconstruction Theorem to completely classify topological equivalence classes of plane holomorphic foliation germs of Poincaré type and discuss a conjecture on the classification in dimension 3.

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DOI : https://doi.org/10.5802/aif.3251
Classification : 32S65,  58K45
Mots clés : germes des feuilletages holomorphes, singularité isolée, equivalence topologique, domaine de Poincaré
@article{AIF_2019__69_2_561_0,
     author = {Eckl, Thomas and L\"onne, Michael},
     title = {Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincar\'e domain},
     journal = {Annales de l'Institut Fourier},
     pages = {561--590},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {2},
     year = {2019},
     doi = {10.5802/aif.3251},
     zbl = {07067412},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3251/}
}
Eckl, Thomas; Lönne, Michael. Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain. Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 561-590. doi : 10.5802/aif.3251. http://archive.numdam.org/articles/10.5802/aif.3251/

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