{
  "id": "2001.02027",
  "version": "v1",
  "published": "2020-01-07T13:43:55.000Z",
  "updated": "2020-01-07T13:43:55.000Z",
  "title": "Twisted conjugacy and commensurability invariance",
  "authors": [
    "Parameswaran Sankaran",
    "Peter Wong"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "A group $G$ is said to have property $R_{\\infty}$ if for every automorphism $\\varphi \\in {\\rm Aut}(G)$, the cardinality of the set of $\\varphi$-twisted conjugacy classes is infinite. Many classes of groups are known to have such property. However, very few examples are known for which $R_{\\infty}$ is {\\it geometric}, i.e., if $G$ has property $R_{\\infty}$ then any group quasi-isometric to $G$ also has property $R_{\\infty}$. In this paper, we give examples of groups and conditions under which $R_{\\infty}$ is preserved under commensurability. The main tool is to employ the Bieri-Neumann-Strebel invariants and other related invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-07T13:43:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E45"
    ],
    "keywords": [
      "commensurability invariance",
      "bieri-neumann-strebel invariants",
      "main tool",
      "twisted conjugacy classes",
      "group quasi-isometric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}