{
  "id": "math/0210315",
  "version": "v3",
  "published": "2002-10-21T03:52:59.000Z",
  "updated": "2003-10-05T10:50:15.000Z",
  "title": "Finite subset spaces of graphs and punctured surfaces",
  "authors": [
    "Christopher Tuffley"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-29.abs.html",
  "journal": "Algebr. Geom. Topol. 3 (2003) 873-904",
  "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 calculate the homology of the finite subset spaces of a connected graph Gamma, and study the maps (exp_k phi)_* induced by a map phi:Gamma -> Gamma' between two such graphs. By homotopy functoriality the results apply to punctured surfaces also. The braid group B_n may be regarded as the mapping class group of an n-punctured disc D_n, and as such it acts on H_*(exp_k D_n). We prove a structure theorem for this action, showing that the image of the pure braid group is nilpotent of class at most floor((n-1)/2).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-10-05T10:50:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "05C10",
      "20F36",
      "55Q52"
    ],
    "keywords": [
      "punctured surfaces",
      "kth finite subset space",
      "pure braid group",
      "non-empty finite subsets",
      "homotopy functor"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10315T"
    }
  }
}