{
  "id": "math/0602631",
  "version": "v2",
  "published": "2006-02-27T21:44:30.000Z",
  "updated": "2006-03-11T18:06:43.000Z",
  "title": "Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants",
  "authors": [
    "Charles Livingston"
  ],
  "comment": "In the first version of this note, the main result was applied to show that the smooth concordance group of topologically slice knots contains a summand isomorphic to a free abelian group on two generators. The author has learned that Manolescu and Owens previously found a knot invariant, based on the Heegaard-Floer Homology of the 2-fold branched cover of the knot, that they used to detect such a summand (see math.GT/0508065). Thus, a consequence of this note is that the work of Hedden-Ording and Manolescu-Owens combines to give a summand that is free on three generators",
  "journal": "Proc. Amer. Math. Soc. 136 (2008) 347-349",
  "categories": [
    "math.GT"
  ],
  "abstract": "As proved by Hedden and Ording, there exist knots for which the Ozsvath-Szabo and Rasmussen smooth concordance invariants, tau and s, differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice. It is shown in this note that a simple manipulation of the Hedden-Ording examples yields a topologically slice Alexander polynomial one knot for which tau and s differ. Manolescu and Owens have previously found a concordance invariant that is independent of both tau and s on knots of polynomial one, and as a consequence have shown that the smooth concordance group of topologically slice knots contains a summand isomorphic to a free abelian group on two generators. It thus follows quickly from the observation in this note that this concordance group contains a subgroup isomorphic to a free abelian group on three generators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-03-11T18:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "slice knots",
      "distinct ozsvath-szabo",
      "rasmussen invariants",
      "free abelian group",
      "topologically slice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2631L"
    }
  }
}