{
  "id": "1305.3455",
  "version": "v2",
  "published": "2013-05-15T13:05:31.000Z",
  "updated": "2014-01-27T12:53:10.000Z",
  "title": "Unknotting number and genus of 3-braid knots",
  "authors": [
    "Eon-Kyung Lee",
    "Sang-Jin Lee"
  ],
  "comment": "published version",
  "journal": "Journal of Knot Theory and Its Ramifications 22, 1350047 (2013)",
  "doi": "10.1142/S0218216513500478",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $u(K)$ and $g(K)$ denote the unknotting number and the genus of a knot $K$, respectively. For a 3-braid knot $K$, we show that $u(K)\\le g(K)$ holds, and that if $u(K)=g(K)$ then $K$ is either a 2-braid knot, a connected sum of two 2-braid knots, the figure-eight knot, a strongly quasipositive knot or its mirror image.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-27T12:53:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "unknotting number",
      "figure-eight knot",
      "mirror image",
      "connected sum"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.3455L"
    }
  }
}