{
  "id": "0807.1187",
  "version": "v2",
  "published": "2008-07-08T10:07:45.000Z",
  "updated": "2008-12-18T04:24:28.000Z",
  "title": "An essential relation between Einstein metrics, volume entropy, and exotic smooth structures",
  "authors": [
    "Michael Brunnbauer",
    "Masashi Ishida",
    "Pablo Suárez-Serrato"
  ],
  "comment": "12 pages, v2; two references added, to appear in Math. Research Letters",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable cohomotopy invariant of Bauer-Furuta in order to present an infinite family of four-manifolds with the following properties: 1) They have positive minimal volume entropy. 2) They satisfy a strict version of the Gromov-Hitchin-Thorpe inequality, with a minimal volume entropy term. 3) They nevertheless admit infinitely many distinct smooth structures for which no compatible Einstein metric exists.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-18T04:24:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "57R57",
      "53C25",
      "57R55"
    ],
    "keywords": [
      "exotic smooth structures",
      "einstein metric",
      "essential relation",
      "minimal volume entropy term",
      "positive minimal volume entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1187B"
    }
  }
}