{
  "id": "2010.10725",
  "version": "v1",
  "published": "2020-10-21T02:34:43.000Z",
  "updated": "2020-10-21T02:34:43.000Z",
  "title": "Hyperbolic jigsaws and families of pseudomodular groups II",
  "authors": [
    "Beicheng Lou",
    "Ser Peow Tan",
    "Anh Duc Vo"
  ],
  "comment": "32 pages, 7 figures, 5 tables",
  "categories": [
    "math.GT",
    "math.GR",
    "math.NT"
  ],
  "abstract": "In our previous paper, we introduced a hyperbolic jigsaw construction and constructed infinitely many non-commensurable, non-uniform, non-arithmetic lattices of $\\mathrm{PSL}(2, \\mathbb{R})$ with cusp set $\\mathbb{Q} \\cup \\{\\infty\\}$ (called pseudomodular groups by Long and Reid), thus answering a question posed by Long and Reid. In this paper, we continue with our study of these jigsaw groups exploring questions of arithmeticity, pseudomodularity, and also related pseudo-euclidean and continued fraction algorithms arising from these groups. We also answer another question of Long and Reid by demonstrating a recursive formula for the tessellation of the hyperbolic plane arising from Weierstrass groups which generalizes the well-known \"Farey addition\" used to generate the Farey tessellation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-21T02:34:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F06",
      "20H05",
      "20H15",
      "30F35",
      "30F60",
      "57M05",
      "57M50"
    ],
    "keywords": [
      "pseudomodular groups",
      "hyperbolic jigsaw construction",
      "jigsaw groups exploring questions",
      "weierstrass groups",
      "non-arithmetic lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}