{
  "id": "math/0604018",
  "version": "v2",
  "published": "2006-04-02T22:30:06.000Z",
  "updated": "2007-05-21T23:25:13.000Z",
  "title": "Combinatorial 3-manifolds with 10 vertices",
  "authors": [
    "Frank H. Lutz"
  ],
  "comment": "9 pages, minor revisions, to appear in Beitr. Algebra Geom",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2\\times S^1$ and 615 triangulations of the twisted sphere product $S^2_\\times_S^1$. All the 3-spheres with up to 10 vertices are shellable, but there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-21T23:25:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57N10"
    ],
    "keywords": [
      "combinatorial",
      "complete enumeration",
      "twisted sphere product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4018L"
    }
  }
}