{
  "id": "2105.07096",
  "version": "v2",
  "published": "2021-05-14T23:38:48.000Z",
  "updated": "2022-06-29T14:55:27.000Z",
  "title": "Thompson-like groups, Reidemeister numbers, and fixed points",
  "authors": [
    "Paula Macedo Lins de Araujo",
    "Altair Santos de Oliveira-Tosti",
    "Yuri Santos Rego"
  ],
  "comment": "v2: 21 pages, 4 figures; Substantially revised, main results strengthened with cohomological versions, improved exposition with more results and expanded literature, new title",
  "categories": [
    "math.GR"
  ],
  "abstract": "We investigate fixed-point properties of automorphisms of groups similar to R. Thompson's group $F$. Revisiting work of Gon\\c{c}alves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the abelianization, implying the so-called property $R_\\infty$. Using the BNS $\\Sigma$-invariant and drawing from works of Gon\\c{c}alves-Sankaran-Strebel and Zaremsky, we show that our tool applies to many $F$-like groups, including Stein's $F_{2,3}$, Cleary's $F_\\tau$, the Lodha-Moore groups, and the braided version of $F$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-29T14:55:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E36",
      "20J05",
      "55M20",
      "57S05"
    ],
    "keywords": [
      "reidemeister numbers",
      "thompson-like groups",
      "fixed points",
      "detect infinite fixed-point sets",
      "tool applies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}