{
  "id": "2304.06276",
  "version": "v1",
  "published": "2023-04-13T05:26:04.000Z",
  "updated": "2023-04-13T05:26:04.000Z",
  "title": "Distinguishing 2-knots admitting circle actions by fundamental groups",
  "authors": [
    "Mizuki Fukuda",
    "Masaharu Ishikawa"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbiolds of cyclic type are obtained as quotient groups of the fundamental groups of the complements of branched twist spins. We use these groups for distinguishing branched twist spins.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-13T05:26:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M05",
      "57M10",
      "57M27"
    ],
    "keywords": [
      "fundamental groups",
      "admitting circle actions",
      "coprime integers",
      "distinguishing branched twist spins",
      "quotient groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}