{
  "id": "2209.01123",
  "version": "v1",
  "published": "2022-09-02T15:33:21.000Z",
  "updated": "2022-09-02T15:33:21.000Z",
  "title": "Direct products of free groups in ${\\rm{Aut}}(F_N)$",
  "authors": [
    "Martin R. Bridson",
    "Richard D. Wade"
  ],
  "comment": "31 pages, 2 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We give a complete description of the embeddings of direct products of nonabelian free groups into ${{\\rm{Aut}}}(F_N)$ and ${{\\rm{Out}}}(F_N)$ when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-02T15:33:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E36",
      "20E05",
      "20E08",
      "20E07"
    ],
    "keywords": [
      "direct products",
      "nonabelian free groups",
      "complete description",
      "direct factors",
      "outer space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}