{"paper":{"title":"Measure equivalence rigidity of $\\mathrm{Out}(F_N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.OA"],"primary_cat":"math.GR","authors_text":"Camille Horbez, Vincent Guirardel","submitted_at":"2021-03-05T14:15:42Z","abstract_excerpt":"We prove that for every $N\\ge 3$, the group $\\mathrm{Out}(F_N)$ of outer automorphisms of a free group of rank $N$ is superrigid from the point of view of measure equivalence: any countable group that is measure equivalent to $\\mathrm{Out}(F_N)$, is in fact virtually isomorphic to $\\mathrm{Out}(F_N)$.\n  We introduce three new constructions of canonical splittings associated to a subgroup of $\\mathrm{Out}(F_N)$ of independent interest. They encode respectively the collection of invariant free splittings, invariant cyclic splittings, and maximal invariant free factor systems. Our proof also reli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.03696","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.03696/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}