{
  "id": "2310.04402",
  "version": "v1",
  "published": "2023-10-06T17:51:57.000Z",
  "updated": "2023-10-06T17:51:57.000Z",
  "title": "An algorithm to decide if an outer automorphism is geometric",
  "authors": [
    "Edgar A. Bering IV",
    "Yulan Qing",
    "Derrick R. Wigglesworth"
  ],
  "comment": "38 page, 3 figures, 2 algorithm displays",
  "categories": [
    "math.GR"
  ],
  "abstract": "An outer automorphism of a free group is geometric if it can be represented by a homeomorphism of a compact surface. Bestvina and Handel gave an algorithmic characterization of geometricity for irreducible automorphisms, using relative train tracks. Using advances in train-track theory, in conjunction with the Guirardel core of tree actions and Nielsen-Thurston theory for surfaces, we give an algorithm that can decide if a general outer automorphism is geometric. The algorithm is constructive and produces a realizing surface homeomorphism if one exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-06T17:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F34",
      "20E36",
      "57M07",
      "20-08"
    ],
    "keywords": [
      "general outer automorphism",
      "compact surface",
      "realizing surface homeomorphism",
      "nielsen-thurston theory",
      "tree actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}