{
  "id": "math/0311371",
  "version": "v1",
  "published": "2003-11-21T03:26:06.000Z",
  "updated": "2003-11-21T03:26:06.000Z",
  "title": "Finite subset spaces of closed surfaces",
  "authors": [
    "Christopher Tuffley"
  ],
  "comment": "40 pages, 5 .eps figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X. We show that the finite subset spaces of a connected 2-complex admit \"lexicographic cell structures\" based on the lexicographic order on I^2 and use these to study the finite subset spaces of closed surfaces. We completely calculate the rational homology of the finite subset spaces of the two-sphere, and determine the top integral homology groups of exp_k Sigma for each k and closed surface Sigma. In addition, we use Mayer-Vietoris arguments and the ring structure of H^*(Sym^k Sigma) to calculate the integer cohomology groups of the third finite subset space of Sigma closed and orientable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-21T03:26:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "54B20",
      "55Q52"
    ],
    "keywords": [
      "closed surface",
      "kth finite subset space",
      "third finite subset space",
      "integral homology groups",
      "integer cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11371T"
    }
  }
}