{
  "id": "0710.1172",
  "version": "v3",
  "published": "2007-10-05T10:28:55.000Z",
  "updated": "2008-03-25T11:04:20.000Z",
  "title": "Combinatorial Alexander Duality -- a Short and Elementary Proof",
  "authors": [
    "Anders Björner",
    "Martin Tancer"
  ],
  "comment": "7 pages, 2 figure; v3: the sign function was simplified",
  "journal": "Discrete Comput. Geom. 42(4) (2009), 586-593",
  "doi": "10.1007/s00454-008-9102-x",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \\subset V: V \\setminus A \\notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-03-25T11:04:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elementary proof",
      "simplicial complex",
      "combinatorial alexander duality states",
      "i-th reduced homology group",
      "reduced cohomology group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1172B"
    }
  }
}