{
  "id": "2407.05574",
  "version": "v1",
  "published": "2024-07-08T03:15:20.000Z",
  "updated": "2024-07-08T03:15:20.000Z",
  "title": "Complete Riemannian 4-manifolds with uniformly positive scalar curvature",
  "authors": [
    "Otis Chodosh",
    "Davi Maximo",
    "Anubhav Mukherjee"
  ],
  "categories": [
    "math.DG",
    "math.GT",
    "math.SG"
  ],
  "abstract": "We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible $4$-manifold uniquely distinguishes the standard $4$-ball up to diffeomorphism among Mazur manifolds and up to homeomorphism in general. We additionally show there exist uncountably many exotic $\\mathbb{R}^4$'s that do not admit such a metric and that any (non-compact) tame $4$-manifold has a smooth structure that does not admit such a metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-08T03:15:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniformly positive scalar curvature",
      "complete riemannian metric",
      "non-compact",
      "manifold uniquely distinguishes",
      "mazur manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}