{
  "id": "1601.02187",
  "version": "v1",
  "published": "2016-01-10T08:31:02.000Z",
  "updated": "2016-01-10T08:31:02.000Z",
  "title": "Relative Nielsen realisation for free products",
  "authors": [
    "Sebastian Hensel",
    "Dawid Kielak"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We generalise the Karrass-Pietrowski-Solitar and the Nielsen realisation theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel-Mosher, as well as a relative version of the Nielsen realisation theorem, which is new even for free groups. The proofs rely on a new version of Stallings' theorem on groups with at least two ends, in which some control over the behaviour of virtual free factors is gained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-10T08:31:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E06"
    ],
    "keywords": [
      "relative nielsen realisation",
      "free products",
      "nielsen realisation theorem",
      "free groups",
      "virtual free factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102187H"
    }
  }
}