{
  "id": "2205.08791",
  "version": "v1",
  "published": "2022-05-18T08:42:41.000Z",
  "updated": "2022-05-18T08:42:41.000Z",
  "title": "Detection of fully irreducible automorphisms in generalized Baumslag-Solitar groups",
  "authors": [
    "Chloé Papin"
  ],
  "comment": "46 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We define fully irreducible automorphisms of generalized Baumslag-Solitar groups in analogy with fully irreducible automorphisms of free groups. We first obtain a characterization of fully irreducible automorphisms analogous to a condition given by Kapovich. Next we discuss the existence of pseudo-periodic conjugacy classes based on the study of Nielsen paths in a train track representative. Finally we give an algorithm which finds out whether an automorphism with a train track representative is pseudo-atoroidal and fully irreducible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-18T08:42:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "20F65"
    ],
    "keywords": [
      "generalized baumslag-solitar groups",
      "train track representative",
      "pseudo-periodic conjugacy classes",
      "free groups",
      "define fully irreducible automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}