{
  "id": "2111.10064",
  "version": "v2",
  "published": "2021-11-19T06:52:11.000Z",
  "updated": "2025-01-30T17:54:09.000Z",
  "title": "Measure equivalence rigidity of the handlebody groups",
  "authors": [
    "Sebastian Hensel",
    "Camille Horbez"
  ],
  "comment": "v2: Revised version after a referee report",
  "categories": [
    "math.GR",
    "math.GT",
    "math.OA"
  ],
  "abstract": "Let $V$ be a connected $3$-dimensional handlebody of finite genus at least $3$. We prove that the handlebody group $\\mathrm{Mod}(V)$ is superrigid for measure equivalence, i.e. every countable group which is measure equivalent to $\\mathrm{Mod}(V)$ is in fact virtually isomorphic to $\\mathrm{Mod}(V)$. Applications include a rigidity theorem for lattice embeddings of $\\mathrm{Mod}(V)$, an orbit equivalence rigidity theorem for free ergodic measure-preserving actions of $\\mathrm{Mod}(V)$ on standard probability spaces, and a $W^*$-rigidity theorem among weakly compact group actions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-30T17:54:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "measure equivalence rigidity",
      "handlebody group",
      "orbit equivalence rigidity theorem",
      "standard probability spaces",
      "free ergodic measure-preserving actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}