{
  "id": "1305.2983",
  "version": "v1",
  "published": "2013-05-14T00:32:37.000Z",
  "updated": "2013-05-14T00:32:37.000Z",
  "title": "Open book decompositions of $\\mathbb{S}^{5}$ and real singularities",
  "authors": [
    "Haydée Aguilar-Cabrera"
  ],
  "comment": "20 pages. arXiv admin note: text overlap with arXiv:1006.0600",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "In this article, we study the topology of the family of real analytic germs $F \\colon (\\mathbb{C}^3,0) \\to (\\mathbb{C},0)$ given by $F(x,y,z)=\\bar{xy}(x^p+y^q)+z^r$ with $p,q,r \\in \\mathbb{N}$, $p,q,r \\geq 2$ and $(p,q)=1$. Such a germ has isolated singularity at 0 and gives rise to a Milnor fibration $\\frac{F}{|F|} \\colon \\mathbb{S}^{5} \\setminus L_F \\to \\mathbb{S}^{1}$. We describe the link $L_F$ as a Seifert manifold and we show that it is always homeomorphic to the link of a complex singularity. However, we prove that in almost all the cases the open-book decomposition of $\\mathbb{S}^{5}$ given by the Milnor fibration of $F$ cannot come from the Milnor fibration of a complex singularity in $\\mathbb{C}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-14T00:32:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S55",
      "57M27"
    ],
    "keywords": [
      "open book decompositions",
      "real singularities",
      "milnor fibration",
      "complex singularity",
      "real analytic germs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2983A"
    }
  }
}