{
  "id": "1908.09046",
  "version": "v1",
  "published": "2019-08-23T22:37:41.000Z",
  "updated": "2019-08-23T22:37:41.000Z",
  "title": "A study of subgroups of right-angled Coxeter groups via Stallings-like techniques",
  "authors": [
    "Pallavi Dani",
    "Ivan Levcovitz"
  ],
  "comment": "52 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We associate a cube complex to any given finitely generated subgroup of a right-angled Coxeter group, called the completion of the subgroup. A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We use completions to show that reflection subgroups are quasiconvex, as are one-ended Coxeter subgroups of a 2-dimensional right-angled Coxeter group. We provide an algorithm that determines whether a given one-ended, 2-dimensional right-angled Coxeter group is isomorphic to some finite-index subgroup of another given right-angled Coxeter group. In addition, we answer several algorithmic questions regarding quasiconvex subgroups. Finally, we give a new proof of Haglund's result that quasiconvex subgroups of right-angled Coxeter groups are separable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-23T22:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F55"
    ],
    "keywords": [
      "right-angled coxeter group",
      "stallings-like techniques",
      "algorithmic questions regarding quasiconvex subgroups",
      "completion",
      "haglunds result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}