{
  "id": "1411.2423",
  "version": "v1",
  "published": "2014-11-10T13:42:58.000Z",
  "updated": "2014-11-10T13:42:58.000Z",
  "title": "The Space of Positive Scalar Curvature Metrics on a Manifold with Boundary",
  "authors": [
    "Mark Walsh"
  ],
  "comment": "43 pages, 31 figures",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "We study the space of Riemannian metrics with positive scalar curvature on a compact manifold with boundary. These metrics extend a fixed boundary metric and take a product structure on a collar neighbourhood of the boundary. We show that the weak homotopy type of this space is preserved by certain surgeries on the boundary in co-dimension at least three. Thus, there is a weak homotopy equivalence between the space of such metrics on a simply connected spin manifold $W$, of dimension $n\\geq 6$ and with simply connected boundary, and the corresponding space of metrics of positive scalar curvature on the standard disk $D^{n}$. Indeed, for certain boundary metrics, this space is weakly homotopy equivalent to the space of all metrics of positive scalar curvature on the standard sphere $S^{n}$. Finally, we prove analogous results for the more general space where the boundary metric is left unfixed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-10T13:42:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J60",
      "55P10"
    ],
    "keywords": [
      "positive scalar curvature metrics",
      "boundary metric",
      "weak homotopy equivalence",
      "weak homotopy type",
      "general space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2423W"
    }
  }
}