{
  "id": "2404.11371",
  "version": "v1",
  "published": "2024-04-17T13:31:26.000Z",
  "updated": "2024-04-17T13:31:26.000Z",
  "title": "The boundary of bordified Outer space",
  "authors": [
    "Karen Vogtmann"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We study the boundary of the \"Jewel space\" $\\mathcal J_n$ constructed in arXiv:1709.01296. This is an equivariant deformation retract of Outer space $CV_n$ on which $Out(F_n)$ acts properly and cocompactly, and is homeomorphic to the Bestvina-Feighn bordification of $CV_n$. In the current paper we analyze the structure of the boundary of $\\mathcal J_n$. We then use the desctiption of the simplicial closure $CV_n^*$ as the sphere complex of a connected sum of $n$ copies of $S^1\\times S^2$ to prove that this boundary is homotopy equivalent to the subcomplex of $CV_n^*$ spanned by vertices at infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-17T13:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E36",
      "20F65",
      "57M07"
    ],
    "keywords": [
      "bordified outer space",
      "equivariant deformation retract",
      "bestvina-feighn bordification",
      "jewel space",
      "current paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}