{"paper":{"title":"Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Matthew C. B. Zaremsky","submitted_at":"2016-07-11T17:20:25Z","abstract_excerpt":"The BNSR-invariants of a group $G$ are a sequence $\\Sigma^1(G)\\supseteq \\Sigma^2(G) \\supseteq \\cdots$ of geometric invariants that reveal important information about finiteness properties of certain subgroups of $G$. We consider the symmetric automorphism group $\\Sigma Aut_n$ and pure symmetric automorphism group $P\\Sigma Aut_n$ of the free group $F_n$, and inspect their BNSR-invariants. We prove that for $n\\ge 2$, all the ``positive'' and ``negative'' character classes of $P\\Sigma Aut_n$ lie in $\\Sigma^{n-2}(P\\Sigma Aut_n)\\setminus \\Sigma^{n-1}(P\\Sigma Aut_n)$. We use this to prove that for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03043","kind":"arxiv","version":1},"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"}