{
  "id": "math/0606435",
  "version": "v2",
  "published": "2006-06-19T03:41:49.000Z",
  "updated": "2007-10-10T03:48:18.000Z",
  "title": "Properties of closed 3-braids",
  "authors": [
    "A. Stoimenow"
  ],
  "comment": "68 pages, 10 figures, 3 tables; rev 10 Oct 07: some reorganization; added sections 4.3, 7.1, 7.7",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid words with Morton-Williams-Franks bound 3 and show that closed positive braids of braid index 3 are closed positive 3-braids. For closed braids on more strings, we study the alternating links occurring. In particular we classify those of braid index 4, and show that their Morton-Williams-Franks inequality is exact. Finally, we use the Burau representation to obtain new braid index criteria, including an efficient 4-braid test.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-10T03:48:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "20F36",
      "32S55"
    ],
    "keywords": [
      "properties",
      "unique incompressible seifert surface",
      "braid index criteria",
      "morton-williams-franks bound",
      "jones polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6435S"
    }
  }
}