{
  "id": "2310.03644",
  "version": "v1",
  "published": "2023-10-05T16:17:55.000Z",
  "updated": "2023-10-05T16:17:55.000Z",
  "title": "Failure of quasi-isometric rigidity for infinite-ended groups",
  "authors": [
    "Nir Lazarovich",
    "Emily Stark"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that an infinite-ended group whose one-ended factors have finite-index subgroups and are in a family of groups with a nonzero multiplicative invariant is not quasi-isometrically rigid. Combining this result with work of the first author proves that a residually-finite multi-ended hyperbolic group is quasi-isometrically rigid if and only if it is virtually free. The proof adapts an argument of Whyte for commensurability of free products of closed hyperbolic surface groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T16:17:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E08",
      "20F67"
    ],
    "keywords": [
      "infinite-ended group",
      "quasi-isometric rigidity",
      "closed hyperbolic surface groups",
      "quasi-isometrically rigid",
      "residually-finite multi-ended hyperbolic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}