{
  "id": "2108.07764",
  "version": "v1",
  "published": "2021-08-17T17:15:41.000Z",
  "updated": "2021-08-17T17:15:41.000Z",
  "title": "Transverse links, open books and overtwisted manifolds",
  "authors": [
    "Rima Chatterjee"
  ],
  "comment": "16 pages, this is a part of a previously arXived paper [arXiv:2011.12217]. Comments welcome",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We prove that transverse links in any contact manifold $(M,\\xi)$ can be realized as a sub-binding of a compatible open book decomposition. We define the support genus of a transverse link and prove that the support genus of the coarse equivalence class of transverse link is zero if there is an overtwisted disk disjoint from it. Next, we find a relationship between the support genus of a Legendrian and transverse link and as a corollary show that a non-loose Legendrian knot will have non-loose transverse push-off if it has non-zero support genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-17T17:15:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K33",
      "57K10"
    ],
    "keywords": [
      "transverse link",
      "overtwisted manifolds",
      "non-zero support genus",
      "non-loose transverse push-off",
      "coarse equivalence class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}