{
  "id": "1106.1472",
  "version": "v3",
  "published": "2011-06-07T23:09:00.000Z",
  "updated": "2011-10-31T03:23:46.000Z",
  "title": "Separating Pants Decompositions in the Pants Complex",
  "authors": [
    "Harold Mark Sultan"
  ],
  "comment": "fixed some typos",
  "journal": "New York Journal of Mathematics, Vol 18, 2012, 79--93",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $\\Gamma(P).$ This perspective provides a convenient way to analyze the maximum distance in the pants complex of any pants decomposition to a pants decomposition containing a non-trivial separating curve for all surfaces of finite type. In the main theorem we provide an asymptotically sharp approximation of this non-trivial distance in terms of the topology of the surface. In particular, for closed surfaces of genus $g$ we show the maximum distance in the pants complex of any pants decomposition to a pants decomposition containing a separating curve grows asymptotically like the function $\\log(g).$",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-31T03:23:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M50",
      "30F60",
      "57M15"
    ],
    "keywords": [
      "pants complex",
      "separating pants decompositions",
      "maximum distance",
      "pants decomposition containing",
      "pants decomposition graph"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1472S"
    }
  }
}