{
  "id": "1004.1552",
  "version": "v3",
  "published": "2010-04-09T13:25:43.000Z",
  "updated": "2012-06-11T07:51:13.000Z",
  "title": "Monodromy and topological classification of germs of holomorphic foliations",
  "authors": [
    "David Marín",
    "Jean-François Mattei"
  ],
  "comment": "To appear in Annales Scientifiques de l'\\'Ecole Normale Sup\\'erieure",
  "categories": [
    "math.DS",
    "math.CV",
    "math.DG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-11T07:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32M25",
      "32S65",
      "37F75"
    ],
    "keywords": [
      "holomorphic foliations",
      "mild hypotheses",
      "complete topological classification",
      "projective holonomy representation",
      "generic conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1552M"
    }
  }
}