{
  "id": "0812.1138",
  "version": "v2",
  "published": "2008-12-05T13:45:10.000Z",
  "updated": "2009-03-04T12:36:05.000Z",
  "title": "A simplicial model for proper homotopy types",
  "authors": [
    "Viêt-Trung Luu"
  ],
  "comment": "9 pages; minor corrections and changes in notation",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "The singular simplicial set Sing(X) of a space X completely captures its weak homotopy type. We introduce a category of_controlled sets_, yielding _simplicial controlled sets_, such that one can functorially produce a singular simplicial controlled set CSing(MaxCtl(X)) from a locally compact X. We then argue that this CSing(MaxCtl(X)) captures the (weak)_proper_ homotopy type of X. Moreover, our techniques strictly generalize the classical simplicial situation: e.g., one obtains, in a unified way, singular homology with compact supports and (Borel-Moore) singular homology with locally finite supports, as well as the corresponding cohomologies.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-04T12:36:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P57",
      "18G30",
      "55U10",
      "55N10"
    ],
    "keywords": [
      "proper homotopy types",
      "simplicial model",
      "simplicial controlled set csing",
      "singular homology",
      "singular simplicial controlled set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1138L"
    }
  }
}