{
  "id": "math/0304086",
  "version": "v2",
  "published": "2003-04-07T05:06:19.000Z",
  "updated": "2003-11-25T02:44:51.000Z",
  "title": "Connectivity of finite subset spaces of cell complexes",
  "authors": [
    "Christopher Tuffley"
  ],
  "comment": "4 pages. v2: retitled; main result strengthened for simply-connected complexes using math.GT/0311371, and problem of strengthening it for m-connected complexes reduced to strengthening it for wedges of (m+1)-spheres",
  "journal": "Pacific J. Math. 217(1):175-179 (2004)",
  "categories": [
    "math.GT"
  ],
  "abstract": "The kth finite subset space of a topological space X is the space exp_k X of non-empty subsets of X of size at most k, topologised as a quotient of X^k. Using results from our earlier paper (math.GT/0210315) on the finite subset spaces of connected graphs we show that the kth finite subset space of a connected cell complex is (k-2)-connected, and (k-1)-connected if in addition the underlying space is simply connected. We expect exp_k X to be (k+m-2)-connected if X is an m-connected cell complex, and reduce proving this to the problem of proving it for finite wedges of (m+1)-spheres. Our results complement a theorem due to Handel that for path-connected Hausdorff X the map on pi_i induced by the inclusion exp_k X --> exp_{2k+1} X is zero for all k and i.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-11-25T02:44:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "54B20",
      "55Q52"
    ],
    "keywords": [
      "kth finite subset space",
      "cell complexes",
      "connectivity",
      "earlier paper",
      "non-empty subsets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4086T"
    }
  }
}