{
  "id": "2007.09725",
  "version": "v1",
  "published": "2020-07-19T17:27:28.000Z",
  "updated": "2020-07-19T17:27:28.000Z",
  "title": "Outer space for RAAGs",
  "authors": [
    "Corey Bregman",
    "Ruth Charney",
    "Karen Vogtmann"
  ],
  "comment": "53 pages, 16 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "For any right-angled Artin group $A_{\\Gamma}$ we construct a finite-dimensional space $\\mathcal{O}_{\\Gamma}$ on which the group $\\text{Out}(A_{\\Gamma})$ of outer automorphisms of $A_{\\Gamma}$ acts properly. We prove that $\\mathcal{O}_{\\Gamma}$ is contractible, so that the quotient is a rational classifying space for $\\text{Out}(A_{\\Gamma})$. The space $\\mathcal{O}_{\\Gamma}$ blends features of the symmetric space of lattices in $\\mathbb{R}^n$ with those of Outer space for the free group $F_n$. Points in $\\mathcal{O}_{\\Gamma}$ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with $A_{\\Gamma}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-19T17:27:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F28",
      "20F36"
    ],
    "keywords": [
      "outer space",
      "locally cat",
      "metric spaces",
      "fundamental group",
      "cube complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}