{
  "id": "1206.3368",
  "version": "v1",
  "published": "2012-06-15T04:30:43.000Z",
  "updated": "2012-06-15T04:30:43.000Z",
  "title": "A note on the homotopy type of the Alexander dual",
  "authors": [
    "Elias Gabriel Minian",
    "Jorge Tomas Rodriguez"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "We investigate the homotopy type of the Alexander dual of a simplicial complex. In general the homotopy type of K does not determine the homotopy type of its dual K*. Moreover, one can construct for each finitely presented group G, a simply connected simplicial complex K with fundamental group isomorphic to G. We study sufficient conditions on K for K* to have the homotopy type of a sphere. We also extend the simplicial Alexander duality to the context of reduced lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-15T04:30:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U05",
      "55P15",
      "57Q05",
      "57Q10",
      "55M05",
      "06A06"
    ],
    "keywords": [
      "homotopy type",
      "simplicial alexander duality",
      "study sufficient conditions",
      "fundamental group isomorphic",
      "simply connected simplicial complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.3368M"
    }
  }
}