{
  "id": "0809.1247",
  "version": "v1",
  "published": "2008-09-07T20:42:38.000Z",
  "updated": "2008-09-07T20:42:38.000Z",
  "title": "Obstructing Sliceness in a Family of Montesinos Knots",
  "authors": [
    "Luke Williams"
  ],
  "comment": "10 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0;[m_1+1,n_1+2],[m_2+1,n_2+2],q), with certain restrictions on m_i, n_i, and q, can be (smoothly) slice. Our techniques use Donaldson's diagonalization theorem and the fact that the 2-fold covers of Montisinos knots bound plumbing 4-manifolds, many of which are negative definite. Some of our examples include knots with signature 0 and square determinant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-07T20:42:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "montesinos knots",
      "obstructing sliceness",
      "donaldsons diagonalization theorem",
      "montisinos knots bound plumbing",
      "pretzel knots"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1247W"
    }
  }
}