{
  "id": "2302.02355",
  "version": "v1",
  "published": "2023-02-05T10:27:16.000Z",
  "updated": "2023-02-05T10:27:16.000Z",
  "title": "A structure theorem for homology 4-manifolds with $g_2\\leq 5$",
  "authors": [
    "Biplab Basak",
    "Sourav Sarkar"
  ],
  "comment": "21 pages and 3 figures",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "Numerous structural findings of homology manifolds have been derived in various ways in relation to $g_2$-values. The homology $4$-manifolds with $g_2\\leq 5$ are characterized combinatorially in this article. It is well-known that all homology $4$-manifolds for $g_2\\leq 2$ are polytopal spheres. We demonstrate that homology $4$-manifolds with $g_2\\leq 5$ are triangulated spheres and are derived from triangulated 4-spheres with $g_2\\leq 2$ by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. The inequality is also quite pronounced for these combinatorial classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-05T10:27:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q25",
      "05E45",
      "55U10",
      "57Q05",
      "57Q15"
    ],
    "keywords": [
      "structure theorem",
      "combinatorial classes",
      "numerous structural findings",
      "homology manifolds",
      "edge contraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}