{
  "id": "1008.1895",
  "version": "v1",
  "published": "2010-08-11T12:33:51.000Z",
  "updated": "2010-08-11T12:33:51.000Z",
  "title": "A counterexample to Wegner's conjecture on good covers",
  "authors": [
    "Martin Tancer"
  ],
  "comment": "8 pages, 3 figures; recommended to print in color",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1975 Wegner conjectured that the nerve of every finite good cover in R^d is d-collapsible. We disprove this conjecture. A good cover is a collection of open sets in R^d such that the intersection of every subcollection is either empty or homeomorphic to an open d-ball. A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at most d-1 which is contained in a unique maximal face.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-11T12:33:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "52A35"
    ],
    "keywords": [
      "wegners conjecture",
      "counterexample",
      "unique maximal face",
      "empty complex",
      "open sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1895T"
    }
  }
}