{
  "id": "1411.1521",
  "version": "v1",
  "published": "2014-11-06T08:18:59.000Z",
  "updated": "2014-11-06T08:18:59.000Z",
  "title": "On a class of $5$-manifolds with $π_1=\\mathbb Z$ with applications to knottings in $S^5$",
  "authors": [
    "Matthias Kreck",
    "Yang Su"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We classify $5$-manifolds with fundamental group $\\mathbb Z$ and $\\pi_{2}$ a finitely generated abelian group in terms of the cup product on the second cohomology of the universal covering. The classification result is applied to study simple knots $k \\colon S^{3} \\subset S^{5}$ and the question, which compact topological or smooth orientable $5$-manifold is a topological or smooth fibre bundle over the circle with simply-connected fibre.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-06T08:18:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R65",
      "57R55"
    ],
    "keywords": [
      "applications",
      "study simple knots",
      "smooth fibre bundle",
      "cup product",
      "second cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1521K"
    }
  }
}