{
  "id": "2305.01451",
  "version": "v1",
  "published": "2023-05-02T14:29:28.000Z",
  "updated": "2023-05-02T14:29:28.000Z",
  "title": "Fixed points of irreducible, displacement one automorphisms of free products",
  "authors": [
    "Matthew Collins"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider the action of outer automorphisms on the deformation space $\\mathcal{O}$ of $G$-trees given by a free product decomposition of a group $G$. We show that an irreducible, displacement 1 automorphism fixes exactly one point in $\\mathcal{O}_1$ (the covolume 1 slice of $\\mathcal{O}$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T14:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E36",
      "20E08"
    ],
    "keywords": [
      "fixed points",
      "displacement",
      "irreducible",
      "free product decomposition",
      "deformation space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}