{
  "id": "1711.08755",
  "version": "v1",
  "published": "2017-11-23T16:11:12.000Z",
  "updated": "2017-11-23T16:11:12.000Z",
  "title": "The geometry of one-relator groups satisfying a polynomial isoperimetric inequality",
  "authors": [
    "Giles Gardam",
    "Daniel J. Woodhouse"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "math.GR"
  ],
  "abstract": "For every pair of positive integers $p > q$ we construct a one-relator group $R_{p,q}$ whose Dehn function is $\\simeq n^\\alpha$ where $\\alpha = 2 \\log_2(2p / q)$. The group $R_{p,q}$ has no subgroup isomorphic to a Baumslag-Solitar group $BS(m,n)$ with $m \\neq \\pm n$, but is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-23T16:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20E06",
      "20F05"
    ],
    "keywords": [
      "polynomial isoperimetric inequality",
      "one-relator groups satisfying",
      "baumslag-solitar group",
      "subgroup isomorphic",
      "dehn function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}