{
  "id": "1510.00089",
  "version": "v1",
  "published": "2015-10-01T01:57:10.000Z",
  "updated": "2015-10-01T01:57:10.000Z",
  "title": "Small Lefschetz fibrations and exotic 4-manifolds",
  "authors": [
    "R. Inanc Baykur",
    "Mustafa Korkmaz"
  ],
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces $\\CP \\# p \\CPb$ for p=7, 8, 9, and to $3 \\CP \\#q \\CPb$ for q =12,...,19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with b^+ at most 3, with one possible exception when b^+=3. Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of $\\CP \\# 4 \\CPb$ and $3 \\CP \\# 6 \\CPb$ from small Lefschetz fibrations over surfaces of higher genera.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T01:57:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small lefschetz fibrations",
      "total spaces",
      "produce positive dehn twist factorizations",
      "derive exotic minimal symplectic",
      "complex rational surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000089B"
    }
  }
}