English

Monodromy and topological classification of germs of holomorphic foliations

Dynamical Systems 2012-06-12 v3 Complex Variables Differential Geometry

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 representation whose topological invariance was conjectured in the eighties by Cerveau and Sad and proved here under mild hypotheses.

Keywords

Cite

@article{arxiv.1004.1552,
  title  = {Monodromy and topological classification of germs of holomorphic foliations},
  author = {David Marín and Jean-François Mattei},
  journal= {arXiv preprint arXiv:1004.1552},
  year   = {2012}
}

Comments

To appear in Annales Scientifiques de l'\'Ecole Normale Sup\'erieure