{"paper":{"title":"Boone-Higman embeddings of $\\mathrm{Aut}(F_n)$ and mapping class groups of punctured surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Francesco Fournier-Facio, James Belk, James Hyde, Matthew C. B. Zaremsky","submitted_at":"2025-03-27T18:01:03Z","abstract_excerpt":"We prove that the groups $\\mathrm{Aut}(F_n)$ satisfy the Boone-Higman conjecture for all $n$, meaning each $\\mathrm{Aut}(F_n)$ embeds in a finitely presented simple group. In fact, we prove that each $\\mathrm{Aut}(F_n)$ satisfies the \"permutational\" Boone-Higman conjecture, which means the simple group in question can be taken to be a twisted Brin-Thompson group. A far-reaching consequence of our approach is that finitely presented twisted Brin-Thompson groups are universal among finitely presented simple groups that are highly transitive. This is evidence toward the Boone-Higman conjecture be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21882","kind":"arxiv","version":2},"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/2503.21882/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"}