{
  "id": "2406.02121",
  "version": "v1",
  "published": "2024-06-04T09:02:39.000Z",
  "updated": "2024-06-04T09:02:39.000Z",
  "title": "Surface groups among cubulated hyperbolic and one-relator groups",
  "authors": [
    "Henry Wilton"
  ],
  "comment": "44 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $\\pi_1(X)$ has a non-free subgroup of infinite index unless $\\pi_1(X)$ is either free or a surface group, answering a question of Wise. A similar result for one-relator groups follows, answering a question posed by several authors. The proof relies on a careful analysis of free and cyclic splittings of cubulated groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-04T09:02:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-relator groups",
      "surface group",
      "cubulated hyperbolic",
      "hyperbolic fundamental group",
      "non-free subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}