{
  "id": "1509.01853",
  "version": "v1",
  "published": "2015-09-06T20:53:50.000Z",
  "updated": "2015-09-06T20:53:50.000Z",
  "title": "Genus two Lefschetz fibration with $b^{+}_{2}=1$ and ${c_1}^{2}=1$",
  "authors": [
    "Anar Akhmedov",
    "Naoyuki Monden"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this article we construct a genus two Lefschetz fibration $f: X \\rightarrow \\mathbb{S}^{2}$ with $b^{+}_{2}(X)=1$ and $c_1^{2}(X)=1$ by applying a lantern substitution to the twisted fiber sum of Matsumoto's well known genus two Lefschetz fibration over $\\mathbb{S}^2$. Moreover, we prove that our fibration admits $-2$ sphere section. We also show that the total space $X$ is symplectically minimal and compute it's fundamental group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-06T20:53:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lefschetz fibration",
      "twisted fiber sum",
      "fibration admits",
      "sphere section",
      "total space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901853A"
    }
  }
}