{
  "id": "1909.02628",
  "version": "v1",
  "published": "2019-09-05T20:52:20.000Z",
  "updated": "2019-09-05T20:52:20.000Z",
  "title": "Connected sum decompositions of high-dimensional manifolds",
  "authors": [
    "Imre Bokor",
    "Diarmuid Crowley",
    "Stefan Friedl",
    "Fabian Hebestreit",
    "Daniel Kasprowski",
    "Markus Land",
    "Johnny Nicholson"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such decompositions exist in higher dimensions and we show that in many settings uniqueness fails in higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-05T20:52:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-dimensional manifolds",
      "higher dimensions",
      "unique connected sum decomposition",
      "classical kneser-milnor theorem says",
      "settings uniqueness fails"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}