{
  "id": "1507.07231",
  "version": "v1",
  "published": "2015-07-26T18:36:37.000Z",
  "updated": "2015-07-26T18:36:37.000Z",
  "title": "Stabilizing Heegaard Splittings of High-Distance Knots",
  "authors": [
    "George Mossessian"
  ],
  "comment": "19 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Suppose $K$ is a knot in $S^3$ with bridge number $n$ and bridge distance greater than $2n$. We show that there are at most ${2n\\choose n}$ distinct minimal genus Heegaard splittings of $S^3\\setminus\\eta(K)$. These splittings can be divided into two families. Two splittings from the same family become equivalent after at most one stabilization. If $K$ has bridge distance at least $4n$, then two splittings from different families become equivalent only after $n-1$ stabilizations. Further, we construct representatives of the isotopy classes of the minimal tunnel systems for $K$ corresponding to these Heegaard surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-26T18:36:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "stabilizing heegaard splittings",
      "high-distance knots",
      "distinct minimal genus heegaard splittings",
      "minimal tunnel systems",
      "bridge distance greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707231M"
    }
  }
}