{
  "id": "1803.08238",
  "version": "v2",
  "published": "2018-03-22T06:09:46.000Z",
  "updated": "2018-09-07T15:47:52.000Z",
  "title": "On generic immersions and totally real embeddings",
  "authors": [
    "Naohiko Kasuya",
    "Masamichi Takase"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GT",
    "math.CV",
    "math.DG"
  ],
  "abstract": "We show that, for a closed orientable n-manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n-1)-space ensures the existence of a totally real embedding into complex n-space. This implies that a closed orientable (4k+1)-manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex 4k-space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-09-07T15:47:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32V40",
      "53C40"
    ],
    "keywords": [
      "totally real embedding",
      "generic immersions",
      "cr-regular embedding",
      "non-vanishing kervaire semi-characteristic possesses",
      "pay special attention"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}