{
  "id": "2105.01967",
  "version": "v1",
  "published": "2021-05-05T10:30:01.000Z",
  "updated": "2021-05-05T10:30:01.000Z",
  "title": "Symmetries of cross caps",
  "authors": [
    "Atsufumi Honda",
    "Kosuke Naokawa",
    "Kentaro Saji",
    "Masaaki Umehara",
    "Kotaro Yamada"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we classify the possible symmetries on cross caps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-05T10:30:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "53A05"
    ],
    "keywords": [
      "symmetries",
      "cross cap singular points",
      "special local coordinate system",
      "coordinate system produce",
      "bruce-wests normal form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}