{
  "id": "math/9911241",
  "version": "v1",
  "published": "1999-11-30T16:50:04.000Z",
  "updated": "1999-11-30T16:50:04.000Z",
  "title": "Knot Concordance and Torsion",
  "authors": [
    "Charles Livingston",
    "Swatee Naik"
  ],
  "comment": "10 pages",
  "journal": "Asian Journal of Mathematics 5 (2001), 161--168",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let K be a knot in the 3-sphere with 2-fold branched covering space M. If for some prime p congruent to 3 mod 4 the p-torsion in the first homology of M is cyclic with odd exponent, then K is of infinite order in the knot concordance group. As one application, recall that the n-twisted double of an arbitrary knot has order 4 in Levine's algebraic concordance group if and only if n is positive and some prime congruent to 3 mod 4 has odd exponent in 4n+1; we show that all such knots are of infinite order in the knot concordance group. As a second application, the 2-bridge knot K(r,s) has infinite order in the knot concordance group if some prime congruent to 3 mod 4 has odd exponent in r.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-30T16:50:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N70"
    ],
    "keywords": [
      "knot concordance group",
      "infinite order",
      "odd exponent",
      "prime congruent",
      "levines algebraic concordance group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11241L"
    }
  }
}