{"paper":{"title":"Rational homological stability for groups of partially symmetric automorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2012-03-21T21:39:58Z","abstract_excerpt":"Let F_{n+m} be the free group of rank n+m, with generators x_1,...,x_{n+m}. An automorphism \\phi of F_{n+m} is called partially symmetric if for each 1 \\le i \\le m, \\phi(x_i) is conjugate to x_j or x_j^{-1} for some 1 \\le j \\le m. Let \\Sigma\\Aut_n^m be the group of partially symmetric automorphisms. We prove that for any m \\ge 0 the inclusion \\Sigma\\Aut_n^m \\to \\Sigma\\Aut_{n+1}^m induces an isomorphism in rational homology for dimensions i satisfying n \\ge (3(i+1)+m)/2, with a similar statement for the groups P\\Sigma\\Aut_n^m of pure partially symmetric automorphisms. We also prove that for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4845","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}