{
  "id": "1102.0890",
  "version": "v2",
  "published": "2011-02-04T12:12:20.000Z",
  "updated": "2011-12-07T10:29:57.000Z",
  "title": "Homogeneous links and the Seifert matrix",
  "authors": [
    "P. M. G. Manchón"
  ],
  "comment": "21 pages, 18 figures, 2 tables. Final version (better organization, including new claim at the end of Section 3, extra information and new references). To appear in Pacific Journal of Mathematics",
  "categories": [
    "math.GT"
  ],
  "abstract": "Homogeneous links were introduced by Peter Cromwell, who proved that the projection surface of these links, that given by the Seifert algorithm, has minimal genus. Here we provide a different proof, with a geometric rather than combinatorial flavor. To do this, we first show a direct relation between the Seifert matrix and the decomposition into blocks of the Seifert graph. Precisely, we prove that the Seifert matrix can be arranged in a block triangular form, with small boxes in the diagonal corresponding to the blocks of the Seifert graph. Then we prove that the boxes in the diagonal has non-zero determinant, by looking at an explicit matrix of degrees given by the planar structure of the Seifert graph. The paper contains also a complete classification of the homogeneous knots of genus one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-07T10:29:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M15"
    ],
    "keywords": [
      "seifert matrix",
      "homogeneous links",
      "seifert graph",
      "block triangular form",
      "projection surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.0890M"
    }
  }
}