{"paper":{"title":"Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\\leq k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Yuka Kotorii","submitted_at":"2013-04-06T09:57:41Z","abstract_excerpt":"J.-B. Meilhan and the second author showed that any Milnor $\\bar{\\mu}$-invariant of length between 3 and $2k+1$ can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all $\\bar{\\mu}$-invariants of length $\\leq k$ vanish. They also showed that their formula does not hold for length $2k+2$. In this paper, we improve their formula to give the $\\bar{\\mu}$-invariants of length $2k+2$ by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by $\\bar{\\mu}$-invariants o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1870","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"}