{
  "id": "1607.05757",
  "version": "v1",
  "published": "2016-07-19T20:53:44.000Z",
  "updated": "2016-07-19T20:53:44.000Z",
  "title": "A characterization of homology manifolds with $g_2\\leq 2$",
  "authors": [
    "Hailun Zheng"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We characterize homology manifolds with $g_2\\leq 2$. Specifically, using retriangulations of simplicial complexes, we give a short proof of Nevo and Novinsky's result on the characterization of homology $(d-1)$-spheres with $g_2=1$ for $d\\geq 5$ and extend it to the class of normal pseudomanifolds. We proceed to prove that every prime homology manifold with $g_2=2$ is obtained by centrally retriangulating a polytopal sphere with $g_2\\leq 1$ along a certain subcomplex. This implies that all homology manifolds with $g_2=2$ are polytopal spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-19T20:53:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "polytopal sphere",
      "prime homology manifold",
      "characterize homology manifolds",
      "normal pseudomanifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}