{
  "id": "2009.05928",
  "version": "v1",
  "published": "2020-09-13T05:46:35.000Z",
  "updated": "2020-09-13T05:46:35.000Z",
  "title": "On special generic maps of rational homology spheres into Euclidean spaces",
  "authors": [
    "Dominik Wrazidlo"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Special generic maps are smooth maps between smooth manifolds with only definite fold points as their singularities. The problem of whether a closed $n$-manifold admits a special generic map into Euclidean $p$-space for $1 \\leq p \\leq n$ was studied by several authors including Burlet, de Rham, Porto, Furuya, \\`{E}lia\\v{s}berg, Saeki, and Sakuma. In this paper, we study rational homology $n$-spheres that admit special generic maps into $\\mathbb{R}^{p}$ for $p<n$. We use the technique of Stein factorization to derive a necessary homological condition for the existence of such maps for odd $n$. We examine our condition for concrete rational homology spheres including lens spaces and total spaces of linear $S^{3}$-bundles over $S^{4}$, and obtain new results on the (non-)existence of special generic maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-13T05:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "58K15",
      "58K30"
    ],
    "keywords": [
      "euclidean spaces",
      "admit special generic maps",
      "concrete rational homology spheres",
      "study rational homology",
      "definite fold points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}