{
  "id": "2212.14383",
  "version": "v1",
  "published": "2022-12-29T17:25:15.000Z",
  "updated": "2022-12-29T17:25:15.000Z",
  "title": "Topology of $3$-manifolds with uniformly positive scalar curvature",
  "authors": [
    "Jian Wang"
  ],
  "comment": "38 pages, 7 figures. Comments Welcome!",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is homeomorphic to an (possibly) infinite connected sum of spherical $3$-manifolds and some copies of $\\mathbb{S}^1\\times \\mathbb{S}^2$. Further, we study an oriented $3$-manifold with mean convex boundary and with uniformly positive scalar curvature. If the boundary is a disjoint union of closed surfaces, then the manifold is an (possibly) infinite conned sum of spherical $3$-manifolds, some handlebodies and some copies of $\\mathbb{S}^1\\times \\mathbb{S}^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-29T17:25:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniformly positive scalar curvature",
      "mean convex boundary",
      "infinite connected sum",
      "complete metric",
      "infinite conned sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}