{
  "id": "1705.05258",
  "version": "v1",
  "published": "2017-05-15T14:17:28.000Z",
  "updated": "2017-05-15T14:17:28.000Z",
  "title": "Topological moduli space for germs of holomorphic foliations",
  "authors": [
    "David Marín",
    "Jean-François Mattei",
    "Éliane Salem"
  ],
  "categories": [
    "math.DS",
    "math.CV",
    "math.DG"
  ],
  "abstract": "This work deals with the topological classification of germs of singular foliations on $(\\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. This moduli space may be an infinite dimensional functional space but under generic conditions we prove that it has finite dimension and we describe its algebraic and topological structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-15T14:17:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "32M25",
      "32S50",
      "32S65"
    ],
    "keywords": [
      "topological moduli space",
      "holomorphic foliations",
      "infinite dimensional functional space",
      "separatrix set",
      "projective holonomy representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}