{
  "id": "0706.3425",
  "version": "v2",
  "published": "2007-06-23T01:56:53.000Z",
  "updated": "2008-03-24T16:18:43.000Z",
  "title": "Twisted conjugacy classes in nilpotent groups",
  "authors": [
    "Daciberg Gonçalves",
    "Peter Wong"
  ],
  "comment": "22 pages; section 6 has been moved to section 2 and minor modification has been made on exposition; to be published in Crelle J",
  "journal": "J. Reine Angew. Math. 633 (2009), 11--27",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "A group is said to have the $R_\\infty$ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether $G$ has the $R_\\infty$ property when $G$ is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer $n\\ge 5$, there is a compact nilmanifold of dimension $n$ on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the $R_\\infty$ property. The $R_{\\infty}$ property for virtually abelian and for $\\mathcal C$-nilpotent groups are also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-24T16:18:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "55M20"
    ],
    "keywords": [
      "twisted conjugacy classes",
      "purely group theoretic proof",
      "finitely generated torsion-free nilpotent group",
      "fixed point free homeomorphism",
      "compact nilmanifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.3425G"
    }
  }
}