{
  "id": "1410.2328",
  "version": "v1",
  "published": "2014-10-09T01:10:13.000Z",
  "updated": "2014-10-09T01:10:13.000Z",
  "title": "Representation stability for homotopy groups of configuration spaces",
  "authors": [
    "Alexander Kupers",
    "Jeremy Miller"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove that the dual rational homotopy groups of the configuration spaces of a 1-connected manifold of dimension at least 3 are uniformly representation stable in the sense of Church, and that their derived dual integral homotopy groups are finitely-generated as FI-modules in the sense of Church-Ellenberg-Farb. This is a consequence of a more general theorem relating properties of the cohomology groups of a 1-connected co-FI-space to properties of its dual homotopy groups. We also discuss several other applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-09T01:10:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "55R35",
      "55S45"
    ],
    "keywords": [
      "configuration spaces",
      "representation stability",
      "dual rational homotopy groups",
      "derived dual integral homotopy groups",
      "dual homotopy groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2328K"
    }
  }
}