{
  "id": "math/0402457",
  "version": "v1",
  "published": "2004-02-27T17:00:58.000Z",
  "updated": "2004-02-27T17:00:58.000Z",
  "title": "Thin presentation of knots and lens spaces",
  "authors": [
    "A. Deruelle",
    "D. Matignon"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.html",
  "journal": "Algebraic and Geometric Topology 3 (2003) 677-707",
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper concerns thin presentations of knots K in closed 3-manifolds M^3 which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of M have only local maxima. If M is a lens space and K has an essential thin presentation with respect to a given standard spine (of lens space M) with only local maxima, then we show that K is a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal intersection between K and such spines to be at least three, and finally, if the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the following inequality: |r| <= 2g, where g is the genus of K_gamma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-27T17:00:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N10",
      "57M15"
    ],
    "keywords": [
      "lens space",
      "paper concerns thin presentations",
      "local maxima",
      "essential thin presentation",
      "r-dehn surgery"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}