{
  "id": "2110.06678",
  "version": "v3",
  "published": "2021-10-13T12:28:06.000Z",
  "updated": "2022-09-25T16:18:08.000Z",
  "title": "Pseudo-Anosovs are exponentially generic in mapping class groups",
  "authors": [
    "Inhyeok Choi"
  ],
  "comment": "Expanded the introduction and elaborated several details. 33 pages and 6 figures. The final version of this paper will appear in Geometry and Topology",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of radius $R$ decrease to 0 as $R$ increases? We show that any finite subset $S'$ of the mapping class group is contained in a finite generating set $S$ such that this proportion decreases exponentially. Our strategy applies to weakly hyperbolic groups and does not refer to the automatic structure of the group.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-09-25T16:18:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "exponentially generic",
      "finite generating set",
      "pseudo-anosovs",
      "automatic structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}