{
  "id": "1510.07564",
  "version": "v1",
  "published": "2015-10-26T17:46:24.000Z",
  "updated": "2015-10-26T17:46:24.000Z",
  "title": "Homology stability for symmetric diffeomorphism and mapping class groups",
  "authors": [
    "Ulrike Tillmann"
  ],
  "comment": "to appear in Math. Proc. Cambridge Philos. Soc",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of $W$ connected sum with $k$ copies of an arbitrary compact smooth manifold $Q$ of the same dimension. The analogues for mapping class groups as well as other generalisations will also be proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T17:46:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "55S05",
      "55R40"
    ],
    "keywords": [
      "mapping class groups",
      "symmetric diffeomorphism",
      "arbitrary compact smooth manifold",
      "smooth compact manifold",
      "satisfy homology stability"
    ],
    "publication": {
      "doi": "10.1017/S0305004115000638",
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2016,
      "month": "Jan",
      "volume": 160,
      "number": 1,
      "pages": 121
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016MPCPS.160..121T"
    }
  }
}