{
  "id": "2212.07085",
  "version": "v1",
  "published": "2022-12-14T08:18:07.000Z",
  "updated": "2022-12-14T08:18:07.000Z",
  "title": "On the fundamental groups of subelliptic varieties",
  "authors": [
    "Yuta Kusakabe"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.CV"
  ],
  "abstract": "We show that the fundamental group of any smooth subelliptic variety is finite. Moreover, it is also proved that every finite group can be realized as the fundamental group of a smooth subelliptic variety. As a consequence, it follows that there exists a smooth subelliptic variety homotopy equivalent to the $n$-sphere if and only if $n>1$. This result can be considered as a negative answer to the algebraic version of Gromov's problem on the homotopy types of Oka manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T08:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "32Q56",
      "14M20",
      "14R10"
    ],
    "keywords": [
      "fundamental group",
      "smooth subelliptic variety homotopy equivalent",
      "algebraic version",
      "finite group",
      "gromovs problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}