{
  "id": "2103.13602",
  "version": "v1",
  "published": "2021-03-25T04:35:11.000Z",
  "updated": "2021-03-25T04:35:11.000Z",
  "title": "Handle decomposition of compact orientable 4-manifolds",
  "authors": [
    "Biplab Basak",
    "Manisha Binjola"
  ],
  "comment": "12 pages, no figure. arXiv admin note: text overlap with arXiv:2011.00761",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "In this article we study a particular class of compact connected orientable PL $4$-manifolds with empty or connected boundary and prove the existence of each handle in its handle decomposition. We particularly work on the compact connected orientable PL $4$-manifolds with rank of fundamental group to be one. Our main result is that if $M$ is a closed connected orientable $4$-manifold then $M$ has either of the following handle decompositions: (i) one $0$-handle, two $1$-handles, $1+\\beta_2(M)$ $2$-handles, one $3$-handle and one $4$-handle, (ii) one $0$-handle, one $1$-handle, $\\beta_2(M)$ $2$-handles, one $3$-handle and one $4$-handle, where $\\beta_2(M)$ denotes the second Betti number of manifold $M$ with $\\mathbb{Z}$ coefficients. Further, we extend this result to any compact connected orientable $4$-manifold $M$ with boundary and give three possible representations of $M$ in terms of handles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T04:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57Q05",
      "57M15",
      "57M50",
      "05C15"
    ],
    "keywords": [
      "handle decomposition",
      "compact orientable",
      "compact connected orientable pl",
      "second betti number",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}