{
  "id": "1808.08894",
  "version": "v1",
  "published": "2018-08-27T15:47:53.000Z",
  "updated": "2018-08-27T15:47:53.000Z",
  "title": "Configuration space in a product",
  "authors": [
    "John D. Wiltshire-Gordon"
  ],
  "comment": "29 pages, 1 figure",
  "categories": [
    "math.AT"
  ],
  "abstract": "Given a finite graph G and a topological space Z, the graphical configuration space Conf(G, Z) is the space of functions V(G) -> Z so that adjacent vertices map to distinct points. We provide a homotopy decomposition of Conf(G, X x Y) in terms of the graphical configuration spaces in X and Y individually. By way of application, we prove a stabilization result for homology of configuration space in X x C^p as p goes to infinity. We also compute the homology of Conf(K_3,T)/T, the space of ordered triples of distinct points in a torus T of rank r, where configurations are considered up to translation. In Section 2, we give an algorithm for computing homology of configuration space in a product of simplicial complexes. The method is applied to products of some sans-serif capital letters in Example 2.12.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-27T15:47:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P10",
      "18G10"
    ],
    "keywords": [
      "distinct points",
      "sans-serif capital letters",
      "graphical configuration space conf",
      "adjacent vertices map",
      "finite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}