{"paper":{"title":"The classification of certain linked $3$-manifolds in $6$-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Sergey Avvakumov","submitted_at":"2014-08-18T08:04:39Z","abstract_excerpt":"We work entirely in the smooth category. An embedding $f:(S^2\\times S^1)\\sqcup S^3\\rightarrow {\\mathbb R}^6$ is {\\it Brunnian}, if the restriction of $f$ to each component is isotopic to the standard embedding. For each triple of integers $k,m,n$ such that $m\\equiv n \\pmod{2}$, we explicitly construct a Brunnian embedding $f_{k,m,n}:(S^2\\times S^1)\\sqcup S^3 \\rightarrow {\\mathbb R}^6$ such that the following theorem holds.\n  Theorem: Any Brunnian embedding $f:(S^2\\times S^1)\\sqcup S^3\\rightarrow {\\mathbb R}^6$ is isotopic to $f_{k,m,n}$ for some integers $k,m,n$ such that $m\\equiv n \\pmod{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3918","kind":"arxiv","version":2},"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"}