{
  "id": "1807.00622",
  "version": "v1",
  "published": "2018-07-02T12:22:29.000Z",
  "updated": "2018-07-02T12:22:29.000Z",
  "title": "On the acylindrical hyperbolicity of automorphism groups of right-angled Artin groups",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "68 pages. Comments are welcome",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In this article, we are interested in the following question: when is the automorphism group of a right-angled Artin group acylindrically hyperbolic? We propose a conjecture, and verify it for molecular graphs, ie., finite simplicial graphs which are connected, triangle-free, square-free and leafless. More precisely, we show that, if $\\Gamma$ is a molecular graph which does not decompose as a star, then the automorphism group $\\mathrm{Aut}(A_\\Gamma)$ is acylindrically hyperbolic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T12:22:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20F28"
    ],
    "keywords": [
      "automorphism group",
      "acylindrical hyperbolicity",
      "molecular graph",
      "right-angled artin group acylindrically hyperbolic",
      "finite simplicial graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 68,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}