{"paper":{"title":"Milnor invariants and the HOMFLYPT polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Jean-Baptiste Meilhan","submitted_at":"2010-02-09T09:15:23Z","abstract_excerpt":"We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \\bar{\\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \\bar{\\mu}-invariant \\bar{\\mu}_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1803","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"}