{
  "id": "1911.05776",
  "version": "v1",
  "published": "2019-11-13T19:32:40.000Z",
  "updated": "2019-11-13T19:32:40.000Z",
  "title": "On the Upsilon invariant of fibered knots and right-veering open books",
  "authors": [
    "Dongtai He",
    "Diana Hubbard",
    "Linh Truong"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a sufficient condition using the Ozsv\\'ath-Stipsicz-Szab\\'o concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on ribbon concordances between fibered knots. Following Baker, we conclude that either fibered knots $K$ in $S^{3}$ satisfying that $\\Upsilon'(t) = -g(K)$ for some $t \\in [0,1)$ are unique in their smooth concordance classes or there exists a counterexample to the Slice-Ribbon Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-13T19:32:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57R17",
      "57R58"
    ],
    "keywords": [
      "fibered knot",
      "right-veering open books",
      "upsilon invariant",
      "ozsvath-stipsicz-szabo concordance invariant upsilon",
      "open book decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}