{
  "id": "1612.07791",
  "version": "v1",
  "published": "2016-12-22T20:52:51.000Z",
  "updated": "2016-12-22T20:52:51.000Z",
  "title": "Infinite loop spaces from operads with homological stability",
  "authors": [
    "Maria Basterra",
    "Irina Bobkova",
    "Kate Ponto",
    "Ulrike Tillmann",
    "Sarah Yeakel"
  ],
  "comment": "This paper represents part of the authors' Women in Topology project",
  "categories": [
    "math.AT"
  ],
  "abstract": "Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space operads in the sense that the group completions of their algebras are infinite loop spaces. The recent, strong homological stability results of Galatius and Randal-Williams for moduli spaces of even dimensional manifolds can be used to construct examples of operads with homological stability. As a consequence the map to $K$-theory defined by the action of the diffeomorphisms on the middle dimensional homology can be shown to be a map of infinite loop spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-22T20:52:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D50",
      "55P47",
      "55P48",
      "57N65"
    ],
    "keywords": [
      "moduli spaces",
      "infinite loop space operads",
      "middle dimensional homology",
      "strong homological stability results",
      "general class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}