{
  "id": "math/9809154",
  "version": "v1",
  "published": "1998-09-28T01:31:17.000Z",
  "updated": "1998-09-28T01:31:17.000Z",
  "title": "On Complexity of the Word Problem in Braid Groups and Mapping Class Groups",
  "authors": [
    "Hessam Hamidi-Tehrani"
  ],
  "comment": "29 pages, 12 figures. To appear in Topology and its applications",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w|^2 g for |w| > log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in the case of the closed surface is O(|w|^2 g^2). We also carry out the same methods for the braid groups, and show that this gives a bound which improves the best known bound in this case; namely, the complexity of the word problem in the n-braid group is O(|w|^2 n), for |w| > log n. We state a similar result for mapping class groups of surfaces with several punctures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-28T01:31:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "68Q25",
      "57S05"
    ],
    "keywords": [
      "mapping class group",
      "word problem",
      "braid groups",
      "complexity",
      "n-braid group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......9154H"
    }
  }
}