{
  "id": "1707.08646",
  "version": "v1",
  "published": "2017-07-26T21:18:48.000Z",
  "updated": "2017-07-26T21:18:48.000Z",
  "title": "Standard Special Generic Maps of Homotopy Spheres into Euclidean Spaces",
  "authors": [
    "Dominik Wrazidlo"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "A so-called special generic map is by definition a map of smooth manifolds all of whose singularities are definite fold points. It is in general an open problem posed by Saeki to determine the set of integers $p$ for which a given homotopy sphere admits a special generic map into $\\mathbb{R}^{p}$. By means of the technique of Stein factorization we introduce and study certain special generic maps of homotopy spheres into Euclidean spaces called standard. Modifying a construction due to Weiss, we show that standard special generic maps give naturally rise to a filtration of the group of homotopy spheres by subgroups that is strongly related to the Gromoll filtration. As an application of our result we deduce the (non-)existence of standard special generic maps on some concrete homotopy spheres such as Milnor spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-26T21:18:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57R60",
      "58K15"
    ],
    "keywords": [
      "standard special generic maps",
      "euclidean spaces",
      "concrete homotopy spheres",
      "definite fold points",
      "homotopy sphere admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}