{
  "id": "math/0407333",
  "version": "v1",
  "published": "2004-07-20T07:29:13.000Z",
  "updated": "2004-07-20T07:29:13.000Z",
  "title": "On word reversing in braid groups",
  "authors": [
    "Patrick Dehornoy",
    "Bert Wiest"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a word by at most a linear factor depending on the group presentation only. We give a counter-example to this conjecture, but, on the other hand, we establish length upper bounds for the case when only right reversing is involved. We also state a new conjecture which would, like the above one, imply that the space complexity of the handle reduction algorithm is linear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-20T07:29:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "braid group",
      "word reversing",
      "handle reduction algorithm",
      "establish length upper bounds",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7333D"
    }
  }
}