{
  "id": "math/0312306",
  "version": "v1",
  "published": "2003-12-16T11:02:44.000Z",
  "updated": "2003-12-16T11:02:44.000Z",
  "title": "Iterated Monodromy Groups",
  "authors": [
    "Volodymyr Nekrashevych"
  ],
  "comment": "about 40 pages, 6 figures",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We associate a group $IMG(f)$ to every covering $f$ of a topological space $M$ by its open subset. It is the quotient of the fundamental group $\\pi_1(M)$ by the intersection of the kernels of its monodromy action for the iterates $f^n$. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamics of $f$ is related to the group. In particular, the Julia set of $f$ can be reconstructed from $\\img(f)$ (from its action on the tree), if $f$ is expanding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-16T11:02:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "37B10",
      "28A80"
    ],
    "keywords": [
      "iterated monodromy group comes",
      "fundamental group",
      "monodromy action",
      "open subset",
      "julia set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12306N"
    }
  }
}