{
  "id": "1811.07202",
  "version": "v2",
  "published": "2018-11-17T18:10:44.000Z",
  "updated": "2021-07-13T21:39:07.000Z",
  "title": "Profinite genus of fundamental groups of torus bundles",
  "authors": [
    "Genildo de Jesus Nery"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper we establish lower and upper bounds for the cardinality of the profinite genus of the fundamental group $\\pi_{1}(M_A)\\cong (\\mathbb{Z} \\times \\mathbb{Z})\\rtimes_{A}\\mathbb{Z}$ of a torus bundle $M_{A}$ in terms of the number of ideal classes of the order $\\mathbb{Z}[\\lambda]$, where $\\lambda$ is an eigenvalue of the matrix $A$ in $\\mathrm{GL}_{2}(\\mathbb{Z})$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-07-13T21:39:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "torus bundle",
      "profinite genus",
      "upper bounds",
      "ideal classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}