{
  "id": "0803.0500",
  "version": "v2",
  "published": "2008-03-04T17:36:51.000Z",
  "updated": "2008-09-17T21:52:20.000Z",
  "title": "Ozsvath-Szabo and Rasmussen invariants of cable knots",
  "authors": [
    "Cornelia A. Van Cott"
  ],
  "comment": "Several corollaries are added, and the exposition is extended",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the behavior of the Ozsvath-Szabo and Rasmussen knot concordance invariants tau and s on K(m,n), the (m,n)-cable of a knot K where m and n are relatively prime. We show that for every knot K and for any fixed positive integer m, both of the invariants evaluated on K(m,n) differ from their value on the torus knot T(m,n) by a fixed constant for all but finitely many n>0. Combining this result together with Hedden's extensive work on the behavior of tau on (m,mr+1)-cables yields bounds on the value of tau on any (m,n)-cable of K. In addition, several of Hedden's obstructions for cables bounding complex curves are extended.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-09-17T21:52:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "rasmussen invariants",
      "cable knots",
      "ozsvath-szabo",
      "rasmussen knot concordance invariants tau",
      "cables bounding complex curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0500V"
    }
  }
}