{
  "id": "1212.1967",
  "version": "v2",
  "published": "2012-12-10T04:08:40.000Z",
  "updated": "2012-12-11T13:36:26.000Z",
  "title": "New Exotic 4-Manifolds via Luttinger Surgery on Lefschetz Fibrations",
  "authors": [
    "Anar Akhmedov",
    "Kadriye Nur Saglam"
  ],
  "comment": "21 pages, 7 figures. One reference added, a few extra clarifying comments added",
  "categories": [
    "math.GT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "In [2], the first author constructed the first known examples of exotic minimal symplectic $\\CP#5\\CPb$ and minimal symplectic 4-manifold that is homeomorphic but not diffeomorphic to $3\\CP#7\\CPb$. The construction in [2] uses Y. Matsumoto's genus two Lefschetz fibrations on $M = \\mathbb{T}^{2}\\times \\mathbb{S}^{2} #4\\CPb$ over $\\mathbb{S}^2$ along with the fake symplectic $\\mathbb{S}^{2} \\times \\mathbb{S}^{2}$ construction given in [1]. The main goal in this paper is to generalize the construction in [2] using the higher genus versions of Matsumoto's fibration constructed by Mustafa Korkmaz and Yusuf Gurtas on $M(k,n) = \\Sigma_{k}\\times \\mathbb{S}^{2} #4n\\CPb$ for any $k \\geq 2$ and $n = 1$, and $k \\geq 1$ and $n \\geq 2$, respectively. Using our building blocks, we also construct symplectic 4-manifolds with the free group of rank $s \\geq 1$ and various other finitely generated groups as the fundamental group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-11T13:36:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lefschetz fibrations",
      "luttinger surgery",
      "construction",
      "exotic minimal symplectic",
      "higher genus versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}