{
  "id": "1205.1565",
  "version": "v3",
  "published": "2012-05-08T00:36:06.000Z",
  "updated": "2013-12-03T18:22:44.000Z",
  "title": "Trisecting 4-manifolds",
  "authors": [
    "David T. Gay",
    "Robion Kirby"
  ],
  "comment": "38 pages, 29 figures; minor improvements to exposition, more examples, and more discussion",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that any smooth, closed, oriented, connected 4--manifold can be trisected into three copies of $\\natural^k (S^1 \\times B^3)$, intersecting pairwise in 3--dimensional handlebodies, with triple intersection a closed 2--dimensional surface. Such a trisection is unique up to a natural stabilization operation. This is analogous to the existence, and uniqueness up to stabilization, of Heegaard splittings of 3--manifolds. A trisection of a 4--manifold $X$ arises from a Morse 2--function $G:X \\to B^2$ and the obvious trisection of $B^2$, in much the same way that a Heegaard splitting of a 3--manifold $Y$ arises from a Morse function $g : Y \\to B^1$ and the obvious bisection of $B^1$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-03T18:22:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "57R45"
    ],
    "keywords": [
      "natural stabilization operation",
      "heegaard splitting",
      "triple intersection",
      "trisecting",
      "morse function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1565G"
    }
  }
}