{
  "id": "1711.09508",
  "version": "v1",
  "published": "2017-11-27T02:22:36.000Z",
  "updated": "2017-11-27T02:22:36.000Z",
  "title": "An invariant of Legendrian and transverse links from open book decompositions of contact 3-manifolds",
  "authors": [
    "Alberto Cavallo"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce a generalization of the Lisca-Ozsv\\'ath-Stipsicz-Szab\\'o Legendrian invariant $\\mathfrak L$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link $L$ in a contact 3-manifold $(M,\\xi)$ with a diagram $D$, given by an open book decomposition of $(M,\\xi)$ adapted to $L$, and we construct a chain complex $cCFL^-(D)$ with a special cycle in it denoted by $\\mathfrak L(D)$. Then, given two diagrams $D_1$ and $D_2$ which represent Legendrian isotopic links, we prove that there is a map between the corresponding chain complexes, that induces an isomorphism in homology and sends $\\mathfrak L(D_1)$ into $\\mathfrak L(D_2)$. Moreover, a connected sum formula is also proved and we use it to give some applications about non-loose Legendrian links; that are links such that the restriction of $\\xi$ on their complement is tight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-27T02:22:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "open book decomposition",
      "transverse links",
      "represent legendrian isotopic links",
      "chain complex",
      "non-loose legendrian links"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}