{
  "id": "2009.11670",
  "version": "v1",
  "published": "2020-09-24T13:17:24.000Z",
  "updated": "2020-09-24T13:17:24.000Z",
  "title": "The Euler characteristic of configuration spaces",
  "authors": [
    "Louis Hainaut"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In this short note we present a generating function computing the compactly supported Euler characteristic $\\chi_c(F(X, n), K^{\\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible complex of sheaves on $X$, and we obtain as a special case a generating function for the Euler characteristic $\\chi(F(X, n))$. We also recall how to use existing results to turn our computation of the Euler characteristic into a computation of the equivariant Euler characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-24T13:17:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80"
    ],
    "keywords": [
      "configuration spaces",
      "equivariant euler characteristic",
      "generating function",
      "compactly supported euler characteristic",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}