Monodromy and topological classification of germs of holomorphic foliations
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, p. 405-445

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.

Nous donnons une classification topologique complète des germes de feuilletages holomorphes dans le plan, sous des conditions de type plutôt générique. Le point-clé est l'introduction d'un nouvel invariant topologique appelé représentation de monodromie. Cette monodromie contient toutes les informations dynamiques pertinentes, en particulier les représentations d'holonomie projective dont l'invariance topologique a été conjecturée dans les années quatre-vingt par Cerveau et Sad et est prouvée ici sous des hypothèses faibles.

DOI : https://doi.org/10.24033/asens.2169
Classification:  37F75,  32M25,  32S65,  34M
Keywords: differential equations, holomorphic foliations, singularities, monodromy, holonomy
@article{ASENS_2012_4_45_3_405_0,
     author = {Mar\'\i n, David and Mattei, Jean-Fran\c cois},
     title = {Monodromy and topological classification of germs of holomorphic foliations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 45},
     number = {3},
     year = {2012},
     pages = {405-445},
     doi = {10.24033/asens.2169},
     mrnumber = {3014482},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_3_405_0}
}
Marín, David; Mattei, Jean-François. Monodromy and topological classification of germs of holomorphic foliations. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, pp. 405-445. doi : 10.24033/asens.2169. http://www.numdam.org/item/ASENS_2012_4_45_3_405_0/

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