{
  "id": "1907.11334",
  "version": "v1",
  "published": "2019-07-25T23:12:13.000Z",
  "updated": "2019-07-25T23:12:13.000Z",
  "title": "Strongly quasipositive quasi-alternating links and Montesinos links",
  "authors": [
    "Idrissa Ba"
  ],
  "comment": "19 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The aim of this article is to give a characterization of strongly quasipositive quasi-alternating links and detect new classes of strongly quasipositive Montesinos links and non-strongly quasipositive Montesinos links. In this direction, we show that, if $L$ is an oriented quasi-alternating link with a quasi-alternating crossing $c$ such that $L_0$ is alternating (where $L_0$ has the induced orientation), then $L$ is definite if and only if it is strongly quasipositive (up to mirroring). We also show that if $L$ is an oriented quasi-alternating link with a quasi-alternating crossing $c$ such that $L_0$ is fibred or more generally has a unique minimal genus Seifert surface (where $L_0$ has the induced orientation), then $L$ is definite if and only if it is strongly quasipositive (up to mirroring).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-25T23:12:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strongly quasipositive quasi-alternating links",
      "unique minimal genus seifert surface",
      "quasipositive montesinos links",
      "oriented quasi-alternating link",
      "induced orientation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}