{
  "id": "1505.06672",
  "version": "v1",
  "published": "2015-05-25T15:54:18.000Z",
  "updated": "2015-05-25T15:54:18.000Z",
  "title": "The Upsilon function of L-space knots is a Legendre transform",
  "authors": [
    "Maciej Borodzik",
    "Matthew Hedden"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of L-space knots, contained in the d-invariants of large surgeries. Generalizations apply for connected sums of L-space knots, which imply that the slice obstruction provided by Upsilon on the subgroup of concordance generated by L-space knots is no finer than that provided by the d-invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T15:54:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "l-space knot",
      "upsilon function",
      "legendre transform",
      "large surgeries",
      "d-invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506672B"
    }
  }
}