{
  "id": "2208.13655",
  "version": "v1",
  "published": "2022-08-29T14:57:12.000Z",
  "updated": "2022-08-29T14:57:12.000Z",
  "title": "$n$-bridge braids and the braid index",
  "authors": [
    "Dane Gollero",
    "Siddhi Krishna",
    "Marissa Loving",
    "Viridiana Neri",
    "Izah Tahir",
    "Len White"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Lorenz knots are an important and well studied family of knots. Birman--Kofman showed that Lorenz knots are in correspondence with $T$-links, which are positive braid closures. They determined the braid index of any $T$-link, based on their defining parameters. In this work, we leverage Birman--Kofman's correspondence to show that 1-bridge braids (and, more generally, $n$-bridge braids) are Lorenz knots. Then, we determine the braid index of 1-bridge braids and $n$-bridge braids; our proof is independent of Birman--Kofman's work, and is explicit, elementary, and effective in nature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-29T14:57:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10"
    ],
    "keywords": [
      "braid index",
      "bridge braids",
      "lorenz knots",
      "leverage birman-kofmans correspondence",
      "positive braid closures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}