{
  "id": "1301.5670",
  "version": "v3",
  "published": "2013-01-23T23:09:38.000Z",
  "updated": "2013-07-18T23:24:07.000Z",
  "title": "H-Spaces, Loop Spaces and the Space of Positive Scalar Curvature Metrics on the Sphere",
  "authors": [
    "Mark Walsh"
  ],
  "comment": "43 pages, 32 figures. In version 2 we added a line to the introduction acknowledging a relevant new result in the field. In version 3, we correct an error in the proof of the second main result",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "For dimensions n greater than or equal to 3, we show that the space of metrics of positive scalar curvature on the n-sphere is homotopy equivalent to a subspace which takes the form of a H-space with a homotopy commutative, homotopy associative product operation. This product operation is based on the connected sum construction. We then exhibit an action of the little n-disks operad on this subspace which, using results of Boardman, Vogt and May implies that when n=3 or n is at least 5, the space of metrics of positive scalar curvature on the n-sphere is weakly homotopy equivalent to an n-fold loop space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-18T23:24:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C99"
    ],
    "keywords": [
      "positive scalar curvature metrics",
      "homotopy equivalent",
      "n-fold loop space",
      "homotopy associative product operation",
      "little n-disks operad"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.5670W"
    }
  }
}