{
  "id": "1403.0690",
  "version": "v1",
  "published": "2014-03-04T05:34:27.000Z",
  "updated": "2014-03-04T05:34:27.000Z",
  "title": "Cords and 1-handles attached to surface-knots",
  "authors": [
    "Seiichi Kamada"
  ],
  "comment": "It will appear in Boletin de la Sociedad Matematica Mexicana",
  "categories": [
    "math.GT"
  ],
  "abstract": "J. Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientable with respect to the orientations of the surfaces. In that case, the equivalence classes of 1-handles correspond to the equivalence classes of cords attached to the surface-knot, and correspond to the double cosets of the peripheral subgroup of the knot group. In this paper, we classify cords and cords with local orientations attached to (possibly non-orientable) surface-knots. And we classify 1-handles attached to surface-knots in the case that the surface-knots are oriented and 1-handles are non-orientable, and in the case that the surface-knots are non-orientable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-04T05:34:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45"
    ],
    "keywords": [
      "surface-knot",
      "equivalence classes",
      "correspond",
      "local orientations",
      "peripheral subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.0690K"
    }
  }
}