{
  "id": "1604.04760",
  "version": "v1",
  "published": "2016-04-16T14:39:48.000Z",
  "updated": "2016-04-16T14:39:48.000Z",
  "title": "On the Upsilon invariant of cable knots",
  "authors": [
    "Wenzhao Chen"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we study the behavior of $\\Upsilon_K(t)$ under the cabling operation, where $\\Upsilon_K(t)$ is the knot concordance invariant defined by Ozsv\\'ath, Stipsicz, and Szab\\'o, associated to a knot $K\\subset S^3$. The main result is an inequality relating $\\Upsilon_K(t)$ and $\\Upsilon_{K_{p,q}}(t)$, which generalizes the inequalities of Hedden \\cite{3} and Van Cott \\cite{17} on the Ozsv\\'ath-Szab\\'o $\\tau$-invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-16T14:39:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57R58"
    ],
    "keywords": [
      "upsilon invariant",
      "cable knots",
      "knot concordance invariant",
      "inequality",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404760C"
    }
  }
}