{
  "id": "2012.00243",
  "version": "v1",
  "published": "2020-12-01T03:37:33.000Z",
  "updated": "2020-12-01T03:37:33.000Z",
  "title": "Levy and Thurston obstructions of finite subdivision rules",
  "authors": [
    "Insung Park"
  ],
  "comment": "36 pages, 11 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a post-critically finite branched covering of the sphere that is a subdivision map of a finite subdivision rule, we define non-expanding spines which determine the existence of a Levy cycle in a non-exhaustive semi-decidable algorithm. Especially when a finite subdivision rule has polynomial growth of edge subdivisions, the algorithm terminates very quickly, and the existence of a Levy cycle is equivalent to the existence of a Thurston obstruction. In order to show the equivalence between Levy and Thurston obstructions, we generalize the arcs intersecting obstruction theorem by Pilgrim and Tan to a graph intersecting obstruction theorem. As a corollary, we prove that for a pair of post-critically finite polynomials, if at least one polynomial has core entropy zero, then their mating has a Levy cycle if and only if the mating has a Thurston obstruction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-01T03:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F15",
      "37F20",
      "20F06"
    ],
    "keywords": [
      "finite subdivision rule",
      "thurston obstruction",
      "levy cycle",
      "graph intersecting obstruction theorem",
      "core entropy zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}