{
  "id": "1811.09055",
  "version": "v1",
  "published": "2018-11-22T08:04:04.000Z",
  "updated": "2018-11-22T08:04:04.000Z",
  "title": "Handle homology of manifolds",
  "authors": [
    "Sebastian Durst",
    "Hansjörg Geiges",
    "Marc Kegel"
  ],
  "comment": "13 pages, 8 figures",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We give an entirely geometric proof, without recourse to cellular homology, of the fact that $\\partial^2=0$ in the chain complex defined by a handle decomposition of a given manifold. Topological invariance of the resulting `handle homology' is a consequence of Cerf theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T08:04:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N35",
      "57R65"
    ],
    "keywords": [
      "handle homology",
      "geometric proof",
      "chain complex",
      "handle decomposition",
      "cerf theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}