{
  "id": "0908.4103",
  "version": "v1",
  "published": "2009-08-27T21:59:37.000Z",
  "updated": "2009-08-27T21:59:37.000Z",
  "title": "Companions of the unknot and width additivity",
  "authors": [
    "Ryan Blair",
    "Maggy Tomova"
  ],
  "comment": "12 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "It has been conjectured that for knots $K$ and $K'$ in $S^3$, $w(K#K')= w(K)+w(K')-2$. Scharlemann and Thompson have proposed potential counterexamples to this conjecture. For every $n$, they proposed a family of knots ${K^n_i}$ for which they conjectured that $w(B^n#K^n_i)=w(K^n_i)$ where $B^n$ is a bridge number $n$ knot. We show that for $n>2$ none of the knots in ${K^n_i}$ produces such counterexamples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-27T21:59:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "width additivity",
      "companions",
      "conjecture",
      "potential counterexamples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.4103B"
    }
  }
}