{
  "id": "math/0405481",
  "version": "v1",
  "published": "2004-05-25T15:29:14.000Z",
  "updated": "2004-05-25T15:29:14.000Z",
  "title": "A factorization of the Conway polynomial and covering linkage invariants",
  "authors": [
    "Tatsuya Tsukamoto",
    "Akira Yasuhara"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "J.P. Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the other is determined by the $\\bar{\\mu}$-invariants of a string link with the link as its closure. We give another description of the latter factor: the determinant of a matrix whose entries are linking pairings in the infinite cyclic covering space of the knot complement, which take values in the quotient field of ${\\Bbb Z}[t,t^{-1}]$. In addition, we give a relation between the Taylor expansion of a linking pairing around $t=1$ and derivation on links which is invented by T.D. Cochran. In fact, the coefficients of the powers of $t-1$ will be the linking numbers of certain derived links in $S^3$. Therefore, the first non-vanishing coefficient of the Conway polynomial is determined by the linking numbers in $S^3$. This generalizes a result of J. Hoste.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-25T15:29:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "conway polynomial",
      "covering linkage invariants",
      "factorization",
      "infinite cyclic covering space",
      "linking numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5481T"
    }
  }
}