{
  "id": "1408.0543",
  "version": "v2",
  "published": "2014-08-03T21:00:28.000Z",
  "updated": "2014-09-05T10:42:30.000Z",
  "title": "The boundary of the outer space of a free product",
  "authors": [
    "Camille Horbez"
  ],
  "comment": "v2: minor revisions",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $G$ be a countable group that splits as a free product of groups of the form $G=G_1\\ast\\dots\\ast G_k\\ast F_N$, where $F_N$ is a finitely generated free group. We identify the closure of the outer space $P\\mathcal{O}(G,\\{G_1,\\dots,G_k\\})$ for the axes topology with the space of projective minimal, \\emph{very small} $(G,\\{G_1,\\dots,G_k\\})$-trees, i.e. trees whose arc stabilizers are either trivial, or cyclic, closed under taking roots, and not conjugate into any of the $G_i$'s, and whose tripod stabilizers are trivial. Its topological dimension is equal to $3N+2k-4$, and the boundary has dimension $3N+2k-5$. We also prove that any very small $(G,\\{G_1,\\dots,G_k\\})$-tree has at most $2N+2k-2$ orbits of branch points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-03T21:00:28.000Z",
      "comment": "43 pages, 9 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-05T10:42:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free product",
      "outer space",
      "branch points",
      "finitely generated free group",
      "arc stabilizers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0543H"
    }
  }
}