{
  "id": "0807.2869",
  "version": "v2",
  "published": "2008-07-17T20:12:43.000Z",
  "updated": "2010-06-15T15:12:27.000Z",
  "title": "Heegaard surfaces and the distance of amalgamation",
  "authors": [
    "Tao Li"
  ],
  "comment": "38 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M_1$ and $M_2$ be orientable irreducible 3--manifolds with connected boundary and suppose $\\partial M_1\\cong\\partial M_2$. Let $M$ be a closed 3--manifold obtained by gluing $M_1$ to $M_2$ along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then $M$ is not homeomorphic to $S^3$ and all small-genus Heegaard splittings of $M$ are standard in a certain sense. In particular, $g(M)=g(M_1)+g(M_2)-g(\\partial M_i)$, where $g(M)$ denotes the Heegaard genus of $M$. This theorem is also true for certain manifolds with multiple boundary components.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-15T15:12:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50",
      "57M25"
    ],
    "keywords": [
      "heegaard surfaces",
      "amalgamation",
      "multiple boundary components",
      "small-genus heegaard splittings",
      "heegaard genus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2869L"
    }
  }
}