{"paper":{"title":"Browder-Livesay filtrations and the example of Cappell and Shaneson","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Du\\v{s}an Repov\\v{s}, Friedrich Hegenbarth, Yuri V. Muranov","submitted_at":"2013-04-28T10:17:42Z","abstract_excerpt":"Let $M^3$ be a 3-dimensional manifold with fundamental group $\\pi_1(M)$ which contains a quaternion subgroup $Q$ of order 8. In 1979 Cappell and Shaneson constructed a nontrivial normal map $\nf\\colon M^3\\times T^2\\to M^3\\times S^2$ which cannot be detected by simply connected surgery obstructions along submanifolds of codimension 0, 1, or 2, but it can be detected by the codimension 3 Kervaire-Arf invariant.\n  The proof of non-triviality of $\\sigma(f)\\in L_5(\\pi_1(M))$ is based on consideration of a Browder-Livesay filtration of a manifold $X$ with $\\pi_1(X)\\cong \\pi_1(M)$. For a Browder-Lives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7449","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"}