{
  "id": "2101.02193",
  "version": "v1",
  "published": "2021-01-06T18:55:31.000Z",
  "updated": "2021-01-06T18:55:31.000Z",
  "title": "JSJ decompositions and polytopes for two-generator one-relator groups",
  "authors": [
    "Giles Gardam",
    "Dawid Kielak",
    "Alan D. Logan"
  ],
  "comment": "37 pages",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "We provide a direct connection between the $\\mathcal{Z}_{\\max}$ (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianisation of rank $2$. We deduce various structural and algorithmic properties, like the existence of a quadratic-time algorithm computing the $\\mathcal{Z}_{\\max}$-JSJ decomposition of such groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T18:55:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E34",
      "20F05",
      "20F65",
      "20F67",
      "20J05"
    ],
    "keywords": [
      "jsj decomposition",
      "hyperbolic two-generator one-relator group",
      "friedl-tillmann polytope",
      "direct connection",
      "algorithmic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}