{"paper":{"title":"The Geometric Invariants of Group Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Nic Koban, Peter Wong","submitted_at":"2012-06-08T18:11:10Z","abstract_excerpt":"In this paper, we compute the {\\Sigma}^n(G) and {\\Omega}^n(G) invariants when 1 \\rightarrow H \\rightarrow G \\rightarrow K \\rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions for G to have the R_{\\infty} property in terms of {\\Omega}^n(H) and {\\Omega}^n(K) when either K is finite or the sequence splits. As an application, we construct a group F \\rtimes? Z_2 where F is the R. Thompson's group F and show that F \\rtimes Z_2 has the R_{\\infty} property while F is not characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1829","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"}