{
  "id": "math/0401075",
  "version": "v1",
  "published": "2004-01-08T15:31:54.000Z",
  "updated": "2004-01-08T15:31:54.000Z",
  "title": "Configuration spaces are not homotopy invariant",
  "authors": [
    "Riccardo Longoni",
    "Paolo Salvatore"
  ],
  "comment": "6 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces $L_{7,1}$ and $L_{7,2}$, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-08T15:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "55S30"
    ],
    "keywords": [
      "configuration spaces",
      "homotopy invariant",
      "massey products",
      "lens spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1075L"
    }
  }
}