{
  "id": "1405.6669",
  "version": "v3",
  "published": "2014-05-26T18:30:07.000Z",
  "updated": "2015-05-19T04:32:39.000Z",
  "title": "Constructing Lefschetz fibrations via Daisy Substitutions",
  "authors": [
    "Anar Akhmedov",
    "Naoyuki Monden"
  ],
  "comment": "27 pages, 6 figures. minor revisions for publication",
  "categories": [
    "math.GT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "We construct new families of non-hyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words $(c_1c_2 \\cdots c_{2g-1}c_{2g}{c_{2g+1}}^2c_{2g}c_{2g-1} \\cdots c_2c_1)^2 = 1$, $(c_1c_2 \\cdots c_{2g}c_{2g+1})^{2g+2} = 1$, and $(c_1c_2 \\cdots c_{2g-1}c_{2g})^{2(2g+1)} = 1$ in the mapping class group $\\Gamma_{g}$ of the closed orientable surface of genus $g$, and study the sections of these Lefschetz fibrations. Furthemore, we show that the total spaces of some of these Lefschetz fibraions are irreducible exotic $4$-manifolds, and compute their Seiberg-Witten invariants. By applying the knot surgery to the family of Lefschetz fibrations obtained from the word $(c_1c_2 \\cdots c_{2g}c_{2g+1})^{2g+2} = 1$ via daisy substitutions, we also construct an infinite family of pairwise non-diffeomorphic irreducible symplectic and non-symplectic $4$-manifolds homeomorphic to $(g^2 - g + 1){\\mathbb{CP}}{}^{2} \\# (3g^{2} - g(k-3) + 2k + 3)\\overline{\\mathbb{CP}}{}^{2}$ for any $g \\geq 3$, and $k = 2, \\cdots, g+1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-29T18:01:41.000Z",
      "comment": "27 pages, 6 figures. Substantially revised and extended from the previous version. Two new subsections added to prove that all our Lefschetz fibrations are non-spin and non-hyperelliptic. The abstract and introduction also revised, and the references added. Comments are welcome!",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-05-19T04:32:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "daisy substitutions",
      "constructing lefschetz fibrations",
      "non-hyperelliptic lefschetz fibrations",
      "total spaces",
      "mapping class group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6669A"
    }
  }
}