{
  "id": "math/0403241",
  "version": "v3",
  "published": "2004-03-15T13:23:39.000Z",
  "updated": "2005-01-27T07:05:50.000Z",
  "title": "Convergence of Baumslag-Solitar groups",
  "authors": [
    "Yves Stalder"
  ],
  "comment": "16 pages, no figure. Notation changes and minor corrections. To appear in Bulletin of the Belgian Mathematical Society -- Simon Stevin",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study convergent sequences of Baumslag-Solitar groups in the space of marked groups. We prove that BS(m,n) --> F_2 for |m|,|n| --> \\infty and BS(1,n) --> Z \\wr Z for |n| --> \\infty. For m fixed, |m|>1, we show that the sequence (BS(m,n))_n is not convergent and characterize many convergent subsequences. Moreover if X_m is the set of BS(m,n)'s for n relatively prime to m and |n|>1, then the map BS(m,n) \\mapsto n extends continuously on the closure of X_m to a surjection onto invertible m-adic integers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-01-27T07:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E06",
      "20E18",
      "20F05"
    ],
    "keywords": [
      "baumslag-solitar groups",
      "convergence",
      "study convergent sequences",
      "convergent subsequences",
      "map bs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3241S"
    }
  }
}