Monodromy and topological classification of germs of holomorphic foliations

David Marín; Jean-François Mattei

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 3, page 405-445
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Marín, David, and Mattei, Jean-François. "Monodromy and topological classification of germs of holomorphic foliations." Annales scientifiques de l'École Normale Supérieure 45.3 (2012): 405-445. <http://eudml.org/doc/272135>.

@article{Marín2012,
abstract = {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.},
author = {Marín, David, Mattei, Jean-François},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {differential equations; holomorphic foliations; singularities; monodromy; holonomy},
language = {eng},
number = {3},
pages = {405-445},
publisher = {Société mathématique de France},
title = {Monodromy and topological classification of germs of holomorphic foliations},
url = {http://eudml.org/doc/272135},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Marín, David
AU - Mattei, Jean-François
TI - Monodromy and topological classification of germs of holomorphic foliations
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 3
SP - 405
EP - 445
AB - 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.
LA - eng
KW - differential equations; holomorphic foliations; singularities; monodromy; holonomy
UR - http://eudml.org/doc/272135
ER -

References

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