{"paper":{"title":"A relationship between twisted conjugacy classes and the geometric invariants $\\Omega^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Nic Koban, Peter Wong","submitted_at":"2009-11-17T19:41:10Z","abstract_excerpt":"A group $G$ is said to have the property $R_\\infty$ if every automorphism $\\phi \\in {\\rm Aut}(G)$ has an infinite number of $\\phi$-twisted conjugacy classes. Recent work of Gon\\c{c}alves and Kochloukova uses the $\\Sigma^n$ (Bieri-Neumann-Strebel-Renz) invariants to show the $R_{\\infty}$ property for a certain class of groups, including the generalized Thompson's groups $F_{n,0}$. In this paper, we make use of the $\\Omega^n$ invariants, analogous to $\\Sigma^n$, to show $R_{\\infty}$ for certain finitely generated groups. In particular, we give an alternate and simpler proof of the $R_{\\infty}$ p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3385","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":""},"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"}