{
  "id": "0906.0137",
  "version": "v1",
  "published": "2009-05-31T17:16:48.000Z",
  "updated": "2009-05-31T17:16:48.000Z",
  "title": "Complexity of relations in the braid group",
  "authors": [
    "Joel Hass",
    "Arkadius Kalka",
    "Tahl Nowik"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that for any given n, there exists a sequence of words a_k in the generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the identity element of B_n, such that the number of braid relations of the form sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass from a_k to the empty word is quadratic with respect to the length of a_k.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-31T17:16:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36"
    ],
    "keywords": [
      "braid group",
      "complexity",
      "identity element",
      "braid relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0137H"
    }
  }
}