{
  "id": "math/0405590",
  "version": "v5",
  "published": "2004-05-31T09:54:57.000Z",
  "updated": "2007-07-10T16:23:07.000Z",
  "title": "Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups",
  "authors": [
    "Alexander Fel'shtyn",
    "Daciberg L. Goncalves"
  ],
  "comment": "20 pages, new sections 6 and 7 are added",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $\\phi:G \\to G$ be a group endomorphism where $G$ is a finitely generated group of exponential growth, and denote by $R(\\phi)$ the number of twisted $\\phi$-conjugacy classes. Fel'shtyn and Hill \\cite{fel-hill} conjectured that if $\\phi$ is injective, then $R(\\phi)$ is infinite. This conjecture is true for automorphisms of non-elementary Gromov hyperbolic groups, see \\cite{ll} and \\cite {fel:1}. It was showed in \\cite {gw:2} that the conjecture does not hold in general. Nevertheless in this paper, we show that the conjecture holds for the Baumslag-Solitar groups $B(m,n)$, where either $|m|$ or $|n|$ is greater than 1 and $|m|\\ne |n|$. We also show that in the cases where $|m|=|n|>1$ or $mn=-1$ the conjecture is true for automorphisms. In addition, we derive few results about the coincidence Reidemeister number.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-07-10T16:23:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "37C25",
      "55M20"
    ],
    "keywords": [
      "twisted conjugacy classes",
      "baumslag-solitar groups",
      "automorphisms",
      "non-elementary gromov hyperbolic groups",
      "coincidence reidemeister number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5590F"
    }
  }
}