{
  "id": "1712.04736",
  "version": "v1",
  "published": "2017-12-13T12:33:28.000Z",
  "updated": "2017-12-13T12:33:28.000Z",
  "title": "Barely CAT(-1) groups are acylindrically hyperbolic",
  "authors": [
    "Anthony Genevois",
    "Arnaud Stocker"
  ],
  "comment": "15 pages, 3 figures. Comments are welcome",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In this paper, we show that, if a group $G$ acts geometrically on a geodesically complete CAT(0) space $X$ which contains at least one point with a CAT(-1) neighborhood, then $G$ must be either virtually cyclic or acylindrically hyperbolic. As a consequence, the fundamental group of a compact Riemannian manifold whose sectional curvature is nonpositive everywhere and negative in at least one point is either virtually cyclic or acylindrically hyperbolic. This statement provides a precise interpretation of an idea expressed by Gromov in his paper Asymptotic invariants of infinite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T12:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67"
    ],
    "keywords": [
      "acylindrically hyperbolic",
      "barely cat",
      "paper asymptotic invariants",
      "virtually cyclic",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}