{
  "id": "2008.02262",
  "version": "v1",
  "published": "2020-08-05T17:44:53.000Z",
  "updated": "2020-08-05T17:44:53.000Z",
  "title": "The braid group $B_3$ in the framework of continued fractions",
  "authors": [
    "Amitesh Datta"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We use the classical interpretation of the braid group $B_3$ as a central extension of the modular group $\\text{PSL}_2\\left(\\mathbb{Z}\\right)$ to establish new and fundamental properties of $B_3$ using the theory of continued fractions. In particular, we give simple and natural linear time algorithms to solve the word and conjugacy problems in $B_3$. The algorithms introduced in this paper are easy to implement and are the most efficient algorithms in the literature to solve these problems in the braid group $B_3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-05T17:44:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "11A55",
      "20F10",
      "20E45",
      "57K10"
    ],
    "keywords": [
      "braid group",
      "continued fractions",
      "natural linear time algorithms",
      "modular group",
      "fundamental properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}