{
  "id": "2001.09712",
  "version": "v1",
  "published": "2020-01-27T12:21:01.000Z",
  "updated": "2020-01-27T12:21:01.000Z",
  "title": "Genus-$3$ Lefschetz Fibrations and Exotic $4$-Manifolds with $b_{2}^{+}=3$",
  "authors": [
    "Tulin Altunoz"
  ],
  "comment": "23 pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We explicitly construct a genus-$3$ Lefschetz fibration over $\\mathbb{S}^{2}$ whose total space is $\\mathbb{T}^{2}\\times \\mathbb{S}^{2}\\# 6\\overline{\\mathbb{C} P^{2}}$ using the monodromy of Matsumoto's genus-$2$ Lefschetz fibration. We then construct more genus-$3$ Lefschetz fibrations whose total spaces are exotic minimal symplectic $4$-manifolds $3 \\mathbb{C} P^{2} \\# q\\overline{\\mathbb{C} P^{2}}$ for $q=13,\\ldots,19$. We also generalize our construction to get genus-$3k$ Lefschetz fibration structure on the $4$-manifold $\\Sigma_{k}\\times \\mathbb{S}^{2}\\# 6\\overline{\\mathbb{C} P^{2}}$ using the generalized Matsumoto's genus-$2k$ Lefschetz fibration. From this generalized version, we derive further exotic $4$-manifolds via Luttinger surgery and twisted fiber sum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-27T12:21:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R17"
    ],
    "keywords": [
      "total space",
      "lefschetz fibration structure",
      "exotic minimal symplectic",
      "luttinger surgery",
      "twisted fiber sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}