We show that the topological equivalence class of holomorphic foliation germs of rank 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 .
Nous démontrons que la classe d’équivalence topologique des germes de feuilletages holomorphiques de rang 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 .
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DOI: 10.5802/aif.3251
Keywords: holomorphic foliation germs, isolated singularity, topological equivalence, Poincaré domain
Mot clés : germes des feuilletages holomorphes, singularité isolée, equivalence topologique, domaine de Poincaré
Eckl, Thomas 1; Lönne, Michael 2
@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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.3251/} }
TY - JOUR AU - Eckl, Thomas AU - Lönne, Michael TI - Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain JO - Annales de l'Institut Fourier PY - 2019 SP - 561 EP - 590 VL - 69 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3251/ DO - 10.5802/aif.3251 LA - en ID - AIF_2019__69_2_561_0 ER -
%0 Journal Article %A Eckl, Thomas %A Lönne, Michael %T Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain %J Annales de l'Institut Fourier %D 2019 %P 561-590 %V 69 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3251/ %R 10.5802/aif.3251 %G en %F AIF_2019__69_2_561_0
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, Volume 69 (2019) no. 2, pp. 561-590. doi : 10.5802/aif.3251. https://aif.centre-mersenne.org/articles/10.5802/aif.3251/
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