{
  "id": "2208.09918",
  "version": "v1",
  "published": "2022-08-21T16:16:39.000Z",
  "updated": "2022-08-21T16:16:39.000Z",
  "title": "Discrete group actions on 3-manifolds and embeddable Cayley complexes",
  "authors": [
    "Agelos Georgakopoulos",
    "George Kontogeorgiou"
  ],
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We prove that a group $\\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following four 3-manifolds: (i) $\\mathbb{S}^3$, (ii) $\\mathbb{R}^3$, (iii) $\\mathbb{S}^2 \\times \\mathbb{R}$, (iv) the complement of a tame Cantor set in $\\mathbb{S}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-21T16:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "57S25",
      "57S30",
      "57S17",
      "57K30",
      "05E45"
    ],
    "keywords": [
      "discrete group actions",
      "embeddable cayley complexes",
      "tame cantor set",
      "natural restrictions",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}