{
  "id": "math/0503229",
  "version": "v2",
  "published": "2005-03-12T00:29:59.000Z",
  "updated": "2006-07-03T02:57:24.000Z",
  "title": "Heegaard genus of the connected sum of m-small knots",
  "authors": [
    "Tsuyoshi Kobayashi",
    "Yo'av Rieck"
  ],
  "comment": "34 pages. Final version, to appear in Communications in Analysis and Geometry",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that if $K_1 \\subset M_1,...,K_n \\subset M_n$ are m-small knots in closed orientable 3-manifolds then the Heegaard genus of $E(#_{i=1}^n K_i)$ is strictly less than the sum of the Heegaard genera of the $E(K_i)$ ($i=1,...,n$) if and only if there exists a proper subset $I$ of $\\{1,...,n\\}$ so that $#_{i \\in I} K_i$ admits a primitive meridian. This generalizes the main result of Morimoto in \\cite{morimoto1}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-03T02:57:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "57M25"
    ],
    "keywords": [
      "m-small knots",
      "heegaard genus",
      "connected sum",
      "heegaard genera",
      "proper subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3229K"
    }
  }
}