{
  "id": "1611.04344",
  "version": "v1",
  "published": "2016-11-14T11:30:04.000Z",
  "updated": "2016-11-14T11:30:04.000Z",
  "title": "Manifolds which admit maps with finitely many critical points into spheres of small dimensions",
  "authors": [
    "Louis Funar",
    "Cornel Pintea"
  ],
  "comment": "21p",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct, for $m\\geq 6$ and $2n\\leq m$, closed manifolds $M^{m}$ with finite nonzero $\\varphi(M^{m},S^{n}$), where $\\varphi(M,N)$ denotes the minimum number of critical points of a smooth map $M\\to N$. We also give some explicit families of examples for even $m\\geq 6, n=3$, taking advantage of the Lie group structure on $S^3$. Moreover, there are infinitely many such examples with $\\varphi(M^{m},S^{n})=1$. Eventually we compute the signature of the manifolds $M^{2n}$ occurring for even $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-14T11:30:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "R70",
      "58K05"
    ],
    "keywords": [
      "critical points",
      "admit maps",
      "small dimensions",
      "lie group structure",
      "finite nonzero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}