{
  "id": "2006.16461",
  "version": "v1",
  "published": "2020-06-30T01:29:31.000Z",
  "updated": "2020-06-30T01:29:31.000Z",
  "title": "Classification of tight contact structures on a solid torus",
  "authors": [
    "Zhenkun Li",
    "Jessica Zhang"
  ],
  "comment": "15 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "It is a basic question in contact geometry to classify all nonisotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, then we need also specify the dividing set on the boundary. In this paper, we answer the classification question completely for the case of a solid torus, by writing down a closed formula for the number of nonisotopic tight contact structures for any possible dividing set on the boundary of the solid torus. Previously only some special cases were known due to work of Honda in 2000 and Honda, Kazez, and Mati\\'c in 2002.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-30T01:29:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K33",
      "57M50"
    ],
    "keywords": [
      "solid torus",
      "nonisotopic tight contact structures",
      "dividing set",
      "basic question",
      "contact geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}