{
  "id": "math/0506558",
  "version": "v1",
  "published": "2005-06-28T03:35:53.000Z",
  "updated": "2005-06-28T03:35:53.000Z",
  "title": "The girth of a Heegaard splitting",
  "authors": [
    "Christopher Jerdonek"
  ],
  "comment": "Ph.D. dissertation, 73 pages, 22 figures (bitmapped EPS, as the arXiv cannot yet accept the vector-based PDF source)",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct simple curves from immersed curves in the setting of handlebodies and Heegaard splittings. We define a measure of complexity we call girth for closed curves in a handlebody. We extend this complexity to Heegaard splittings and pose a conjecture about all Heegaard splittings. We prove a test case of this conjecture. Let S be a compact surface embedded in the boundary of a handlebody H. Then the minimum girth over all curves in S can be achieved by a simple closed curve. We also present algorithms to compute the girth of curves and surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-28T03:35:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50"
    ],
    "keywords": [
      "heegaard splitting",
      "construct simple curves",
      "handlebody",
      "complexity",
      "conjecture"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6558J"
    }
  }
}