{
  "id": "1805.03544",
  "version": "v1",
  "published": "2018-05-09T14:07:49.000Z",
  "updated": "2018-05-09T14:07:49.000Z",
  "title": "Simply-connected open 3-manifolds with slow decay of positive scalar curvature",
  "authors": [
    "Jian Wang"
  ],
  "comment": "10 pages, comments are welcomed!",
  "categories": [
    "math.DG"
  ],
  "abstract": "The goal of this paper is to investigate the topological structure of open simply-connected 3-manifolds whose scalar curvature has a slow decay at infinity. In particular, we show that the Whitehead manifold does not admit a complete metric, whose scalar curvature decays slowly, and in fact that any contractible complete 3-manifolds with such a metric is homeomorphic to $\\mathbb{R}^{3}$. Furthermore, using this result, we prove that any open simply-connected 3-manifold $M$ with $\\pi_{2}(M)=\\mathbb{Z}$ and a complete metric as above, is homeomorphic to $\\mathbb{S}^{2}\\times \\mathbb{R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-09T14:07:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive scalar curvature",
      "slow decay",
      "simply-connected open",
      "complete metric",
      "scalar curvature decays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}