{
  "id": "1811.09220",
  "version": "v1",
  "published": "2018-11-22T16:07:17.000Z",
  "updated": "2018-11-22T16:07:17.000Z",
  "title": "Subgroups of word hyperbolic groups in dimension $2$",
  "authors": [
    "Shivam Arora",
    "Eduardo Martínez-Pedroza"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A result of Gersten states that if $G$ is a hyperbolic group with integral cohomological dimension $\\mathsf{cd}_{\\mathbb{Z}}(G)=2$ then every finitely presented subgroup is hyperbolic. We generalize this result for the rational case $\\mathsf{cd}_{\\mathbb{Q}}(G)=2$. In particular, our result applies to the class of torsion-free hyperbolic groups $G$ with $\\mathsf{cd}_{\\mathbb{Z}}(G)=3$ and $\\mathsf{cd}_{\\mathbb{Q}}(G)=2$ discovered by Bestvina and Mess.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T16:07:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20F69",
      "20J05",
      "57M07"
    ],
    "keywords": [
      "word hyperbolic groups",
      "torsion-free hyperbolic groups",
      "integral cohomological dimension",
      "gersten states",
      "rational case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}