{
  "id": "math/9906084",
  "version": "v1",
  "published": "1999-06-12T18:20:10.000Z",
  "updated": "1999-06-12T18:20:10.000Z",
  "title": "Pants Decompositions of Surfaces",
  "authors": [
    "Allen Hatcher"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems form the vertices of a 2-complex, whose edges correspond to certain simple moves in which only one curve changes, and whose 2-cells correspond to certain elementary cycles of simple moves. The main theorem is that this 2-complex is simply-connected. Thus any two pants decompositions of a surface are joinable by a sequence of simple moves, and any two such sequences of simple move are related by the elementary relations. The proof is similar to the proof, in a 1980 paper with W. Thurston, of an analogous result for curve systems with connected genus zero complement. [The present paper is essentially an excerpt from a joint paper with P. Lochak and L. Schneps which is to appear in Crelle's Journal.]",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-06-12T18:20:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pants decompositions",
      "simple move",
      "connected genus zero complement",
      "curve systems form",
      "disjoint simple closed curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6084H"
    }
  }
}