{
  "id": "2309.16613",
  "version": "v1",
  "published": "2023-09-28T17:12:36.000Z",
  "updated": "2023-09-28T17:12:36.000Z",
  "title": "Conjugacy in Rearrangement Groups of Fractals",
  "authors": [
    "Matteo Tarocchi"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We describe a method for solving the conjugacy problem in a vast class of rearrangement groups of fractals, a family of Thompson-like groups introduced in 2019 by Belk and Forrest. We generalize the methods of Belk and Matucci for the solution of the conjugacy problem in Thompson groups $F$, $T$ and $V$ via strand diagrams. In particular, we solve the conjugacy problem for the Basilica, the Airplane, the Vicsek and the Bubble Bath rearrangement groups and for the groups $QV$ (also known as $QAut(\\mathcal{T}_{2,c})$), $\\tilde{Q}V$, $QT$, $\\tilde{Q}T$ and $QF$, and we provide a new solution to the conjugacy problem for the Houghton groups and for the Higman-Thompson groups, where conjugacy was already known to be solvable. Our methods involve two distinct rewriting systems, one of which is an instance of a graph rewriting system, whose confluence in general is of interest in computer science.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-28T17:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "28A80",
      "20E45",
      "20F38",
      "20F65"
    ],
    "keywords": [
      "conjugacy problem",
      "bubble bath rearrangement groups",
      "houghton groups",
      "strand diagrams",
      "higman-thompson groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}