{
  "id": "2410.16900",
  "version": "v1",
  "published": "2024-10-22T11:06:47.000Z",
  "updated": "2024-10-22T11:06:47.000Z",
  "title": "On elliptic surfaces which have no 1-handles",
  "authors": [
    "Daisuke Kusuda"
  ],
  "comment": "19 pages, 26 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Gompf conjectured that the elliptic surface $E(n)_{p,q}$ has no handle decomposition without 1- and 3-handles. We prove that each of the elliptic surfaces $E(n)_{5,6}$, $E(n)_{6,7}$, $E(n)_{7,8}$ and $E(n)_{8,9}$ has a handle decomposition without 1-handles for $n\\geq4$, $n\\geq 5$, $n\\geq 9$ and $n\\geq 24$, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-22T11:06:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R19"
    ],
    "keywords": [
      "elliptic surface",
      "handle decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}