{
  "id": "1612.04424",
  "version": "v1",
  "published": "2016-12-13T22:51:46.000Z",
  "updated": "2016-12-13T22:51:46.000Z",
  "title": "A positive characterization of rational maps",
  "authors": [
    "Dylan P. Thurston"
  ],
  "comment": "32 pages, 6 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "When is a topological branched self-cover of the sphere equivalent to a rational map on CP^1? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive criterion: the branched self-cover is equivalent to a rational map if and only if there is an elastic spine that gets \"looser\" under backwards iteration. This completes a series announced in arXiv:1502.02561 and started in arXiv:1507.05294 and arXiv:1607.00340.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-13T22:51:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37E25",
      "37F30"
    ],
    "keywords": [
      "rational map",
      "positive characterization",
      "branched self-cover",
      "william thurston gave",
      "sphere equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}