{
  "id": "1408.1903",
  "version": "v3",
  "published": "2014-08-08T16:27:35.000Z",
  "updated": "2014-08-29T04:01:10.000Z",
  "title": "Homological Stability For The Moduli Spaces of Products of Spheres",
  "authors": [
    "Nathan Perlmutter"
  ],
  "comment": "32 pages: this article supersedes arXiv:1311.5648 . Changed the introduction and made some changes to the exposition throughout. Comments are welcome",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\\times S^{q}$, for $p < q < 2p - 2$. This result is analogous to recent results of S. Galatius and O. Randal-Williams regarding the homological stability for the moduli spaces of manifolds of dimension $2n > 4$, with respect to forming connected sums with $S^{n}\\times S^{n}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-11T17:57:50.000Z",
      "comment": "28 pages: this article supersedes arXiv:1311.5648 . Fixed a typo in the abstract and in the introduction regarding the dimensional range of the main result. Comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-08-29T04:01:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "57R15",
      "57R56",
      "55P47"
    ],
    "keywords": [
      "moduli spaces",
      "homological stability theorem",
      "high-dimensional",
      "highly connected manifolds",
      "forming connected sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1903P"
    }
  }
}