{
  "id": "2001.02822",
  "version": "v1",
  "published": "2020-01-09T03:34:33.000Z",
  "updated": "2020-01-09T03:34:33.000Z",
  "title": "Twisted conjugacy in free products",
  "authors": [
    "Daciberg Goncalves",
    "Parameswaran Sankaran",
    "Peter Wong"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\phi:G\\to G$ be an automorphism of a group which is a free-product of finitely many groups each of which is freely indecomposable and contains a proper finite index subgroup. We show that $G$ has infinitely many $\\phi$-twisted conjugacy classes. As an application, we show that if $G$ is the fundamental group of three-manifold which is not irreducible, then $G$ has the $R_\\infty$-property, that is, there are infinitely many $\\phi$-twisted conjugacy classes in $G$ for every automorphism $\\phi$ of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-09T03:34:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "22E40",
      "20E36"
    ],
    "keywords": [
      "free products",
      "twisted conjugacy classes",
      "proper finite index subgroup",
      "automorphism",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}