{
  "id": "1403.2334",
  "version": "v2",
  "published": "2014-03-10T18:37:48.000Z",
  "updated": "2016-02-04T00:38:25.000Z",
  "title": "Homological stability for moduli spaces of high dimensional manifolds. I",
  "authors": [
    "Soren Galatius",
    "Oscar Randal-Williams"
  ],
  "comment": "43 pages, 2 figures; this article supersedes arXiv:1203.6830. v2 proves a stronger statement and combines better with arXiv:1601.00232",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We prove a homological stability theorem for moduli spaces of simply-connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \\times S^n$. This is analogous to Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of the moduli spaces of manifolds diffeomorphic to connected sums of $S^n \\times S^n$ in a range of degrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-10T18:37:48.000Z",
      "abstract": "We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S^n x S^n. This is analogous to Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of the moduli spaces of manifolds diffeomorphic to connected sums of S^n x S^n in a range of degrees.",
      "comment": "34 pages, 1 figure; this article supersedes arXiv:1203.6830",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-04T00:38:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R90",
      "57R15",
      "57R56",
      "55P47"
    ],
    "keywords": [
      "high dimensional manifolds",
      "moduli spaces",
      "connected sum",
      "harers stability theorem",
      "dimension 2n"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2334G"
    }
  }
}