{
  "id": "1906.04128",
  "version": "v1",
  "published": "2019-06-10T17:03:53.000Z",
  "updated": "2019-06-10T17:03:53.000Z",
  "title": "Contractible 3-manifold and Positive scalar curvature (II)",
  "authors": [
    "Jian Wang"
  ],
  "comment": "38 Pages, 7 Figures. Comments are welcomed!",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "In this article, we are interested in the question whether any complete contractible $3$-manifold of positive scalar curvature is homeomorphic to $\\mathbb{R}^{3}$. We study the fundamental group at infinity, $\\pi_{1}^{\\infty}$, and its relationship with the existence of complete metrics of positive scalar curvature. We prove that a complete contractible $3$-manifold with positive scalar curvature and trivial $\\pi^{\\infty}_{1}$ is homeomorphic to $\\mathbb{R}^{3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-10T17:03:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive scalar curvature",
      "fundamental group",
      "complete contractible",
      "complete metrics",
      "homeomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}