{
  "id": "0811.0641",
  "version": "v3",
  "published": "2008-11-05T14:55:26.000Z",
  "updated": "2009-01-06T01:45:40.000Z",
  "title": "Giroux correspondence, confoliations, and symplectic structures on S^1 x M",
  "authors": [
    "Jin Hong Kim"
  ],
  "comment": "17 pages; Sec.3 rewritten for more clarity",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Let M be a closed oriented 3-manifold such that S^1 x M admits a symplectic structure w. The goal of this paper is to show that M is a fiber bundle over S^1. The basic idea is to use the obvious S^1-action on S^1 x M by rotating the first factor, and one of the key steps is to show that the S^1-action on S^1 x M is actually symplectic with respect to a symplectic form cohomologous to w. We achieve it by crucially using the recent result or its relative version of Giroux about one-to-one correspondence between open book decompositions of M up to positive stabilization and co-oriented contact structures on M up to contact isotopy.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-01-06T01:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic structure",
      "giroux correspondence",
      "confoliations",
      "open book decompositions",
      "first factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0641K"
    }
  }
}