{
  "id": "2403.15809",
  "version": "v1",
  "published": "2024-03-23T11:38:49.000Z",
  "updated": "2024-03-23T11:38:49.000Z",
  "title": "The Goeritz groups of $(1,1)$-decompositions",
  "authors": [
    "Yuya Koda",
    "Yuki Tanaka"
  ],
  "comment": "16 pages, 13 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A $(g, n)$-decomposition of a link $L$ in a closed orientable $3$-manifold $M$ is a decomposition of $M$ by a closed orientable surface of genus $g$ into two handebodies each of which intersects the link $L$ in $n$ trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair $(M, L)$ preserving the decomposition. We compute the Goeritz groups of all $(1,1)$-decompositions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-23T11:38:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K20",
      "57K10"
    ],
    "keywords": [
      "goeritz group",
      "decomposition",
      "trivial arcs",
      "isotopy classes",
      "handebodies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}