{
  "id": "1406.0902",
  "version": "v2",
  "published": "2014-06-03T23:08:14.000Z",
  "updated": "2015-09-03T14:18:16.000Z",
  "title": "The solvable length of groups of local diffeomorphisms",
  "authors": [
    "Javier Ribón"
  ],
  "comment": "40 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we show that $2n+1$ is the sharpest upper bound for the derived length of solvable subgroups of the group $\\mathrm{Diff}({\\mathbb C}^{n},0)$ of local complex analytic diffeomorphisms for $n=2,3,4,5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-03T23:08:14.000Z",
      "title": "The solvable length of a solvable group of local diffeomorphisms",
      "abstract": "We show that $2n+1$ is the sharpest upper bound for the derived length of solvable subgroups of the group $\\mathrm{Diff}({\\mathbb C}^{n},0)$ of local complex analytic diffeomorphisms for $n=2,3,4,5$.",
      "comment": "33 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-03T14:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "20F16",
      "20F14",
      "32H50"
    ],
    "keywords": [
      "local diffeomorphisms",
      "solvable group",
      "solvable length",
      "local complex analytic diffeomorphisms",
      "sharpest upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.0902R"
    }
  }
}