{
  "id": "2012.00432",
  "version": "v1",
  "published": "2020-12-01T12:02:32.000Z",
  "updated": "2020-12-01T12:02:32.000Z",
  "title": "On the homotopy type of the space of metrics of positive scalar curvature",
  "authors": [
    "Johannes Ebert",
    "Michael Wiemeler"
  ],
  "categories": [
    "math.DG",
    "math.AT",
    "math.GT"
  ],
  "abstract": "The main result of this paper is that when $M_0$, $M_1$ are two simply connected spin manifolds of the same dimension $d \\geq 5$ which both admit a metric of positive scalar curvature, the spaces $\\mathcal{R}^+(M_0)$ and $\\mathcal{R}^+(M_1)$ of such metrics are homotopy equivalent. This supersedes a previous result of Chernysh and Walsh which gives the same conclusion when $M_0$ and $M_1$ are also spin cobordant. We also prove an analogous result for simply connected manifolds which do not admit a spin structure; we need to assume that $d \\neq 8$ in that case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-01T12:02:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive scalar curvature",
      "homotopy type",
      "spin cobordant",
      "homotopy equivalent",
      "simply connected spin manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}