{
  "id": "1005.2300",
  "version": "v2",
  "published": "2010-05-13T11:19:17.000Z",
  "updated": "2010-10-25T10:49:01.000Z",
  "title": "Topology of configuration space of two particles on a graph, II",
  "authors": [
    "Michael Farber",
    "Elizabeth Hanbury"
  ],
  "comment": "24 pages, 12 figures; Section 7 revised in v2, published version",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We introduce a linking bilinear form on the homology group of the graph with values in the cokernel of the intersection form (introduced in Part I of this work). For a large class of graphs, which we call mature graphs, we give explicit expressions for the homology groups of the configuration space. We show that under a simple condition, adding an edge to a mature graph yields another mature graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-25T10:49:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "57M15"
    ],
    "keywords": [
      "configuration space",
      "homology group",
      "mature graph yields",
      "simple condition",
      "distinct points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.2300F"
    }
  }
}