{
  "id": "1211.5103",
  "version": "v1",
  "published": "2012-11-21T18:01:57.000Z",
  "updated": "2012-11-21T18:01:57.000Z",
  "title": "The topology of real suspension singularities of type $f \\bar{g}+z^n$",
  "authors": [
    "Haydée Aguilar-Cabrera"
  ],
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "In this article we study the topology of a family of real analytic germs $F \\colon (\\mathbb{C}^3,0) \\to (\\mathbb{C},0)$ with isolated critical point at 0, given by $F(x,y,z)=f(x,y)\\bar{g(x,y)}+z^r$, where $f$ and $g$ are holomorphic, $r \\in \\mathbb{Z}^+$ and $r \\geq 2$. We describe the link $L_F$ as a graph manifold using its natural open book decomposition, related to the Milnor fibration of the map-germ $f \\bar{g}$ and the description of its monodromy as a quasi-periodic diffeomorphism through its Nielsen invariants. Furthermore, such a germ $F$ gives rise to a Milnor fibration $\\frac{F}{|F|} \\colon \\mathbb{S}^5 \\setminus L_F \\to \\mathbb{S}^1$. We present a join theorem, which allows us to describe the homotopy type of the Milnor fibre of $F$ and we show some cases where 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": "2012-11-21T18:01:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S25",
      "32S55",
      "32S50",
      "57M27"
    ],
    "keywords": [
      "real suspension singularities",
      "milnor fibration",
      "singularity",
      "natural open book decomposition",
      "real analytic germs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5103A"
    }
  }
}