{
  "id": "0709.2174",
  "version": "v1",
  "published": "2007-09-13T21:30:52.000Z",
  "updated": "2007-09-13T21:30:52.000Z",
  "title": "Topological rigidity for holomorphic foliations",
  "authors": [
    "Mahdi Teymuri Garakani"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\\mathbb{C}P(2)$. Let $\\{\\mathcal{F}_t\\}_{t \\in \\mathbb{D}_{\\epsilon}}$ be topological trivial (in $\\mathbb{C}^2$) analytic deformation of a foliation $\\mathcal{F}_0$ on $\\mathbb{C}^2$. We show that under some dynamical restriction on $\\mathcal{F}_0$, we have two possibilities: $\\mathcal{F}_0$ is a Darboux (logarithmic) foliation, or $\\{\\mathcal{F}_t\\}_{t \\in \\mathbb{D}_{\\epsilon}}$ is an unfolding. We obtain in this way a link between the analytical classification of the unfolding and the one of its germs at the singularities on the infinity line. Also we prove that a finitely generated subgroup of $\\mathrm{Diff}(\\mathbb{C}^n,0)$ with polynomial growth is solvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-13T21:30:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75"
    ],
    "keywords": [
      "holomorphic foliations",
      "topological rigidity",
      "study analytic deformations",
      "polynomial growth",
      "infinity line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2174T"
    }
  }
}