{
  "id": "2005.04173",
  "version": "v1",
  "published": "2020-05-08T17:15:26.000Z",
  "updated": "2020-05-08T17:15:26.000Z",
  "title": "On the Support Genus of Legendrian Knots",
  "authors": [
    "Sinem Onaran"
  ],
  "comment": "12 pages, 15 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "In this paper, we show that any topological knot or link in $S^1 \\times S^2$ sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in $S^1 \\times S^2$ has a Legendrian representative having support genus zero. We also show this holds for some knots and links in the lens spaces $L(p,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-08T17:15:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17"
    ],
    "keywords": [
      "legendrian knots",
      "support genus zero",
      "open book decomposition",
      "positive dehn twists",
      "link type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}