{
  "id": "0907.2444",
  "version": "v2",
  "published": "2009-07-14T20:03:06.000Z",
  "updated": "2012-01-02T21:56:11.000Z",
  "title": "Deforming three-manifolds with positive scalar curvature",
  "authors": [
    "Fernando Coda Marques"
  ],
  "comment": "46 pages, 14 figures. An entire section and pictures were added. To appear in Annals of Mathematics",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact 3-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically flat solutions to the vacuum Einstein constraint equations on $\\mathbb{R}^3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-02T21:56:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive scalar curvature",
      "deforming three-manifolds",
      "vacuum einstein constraint equations",
      "hamiltons ricci flow",
      "trace-free asymptotically flat solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2444C"
    }
  }
}