{"paper":{"title":"Goldman-Turaev formality implies Kashiwara-Vergne","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.QA"],"primary_cat":"math.GT","authors_text":"Anton Alekseev, Florian Naef, Nariya Kawazumi, Yusuke Kuno","submitted_at":"2018-12-04T01:31:13Z","abstract_excerpt":"Let $\\Sigma$ be a compact connected oriented 2-dimensional manifold with non-empty boundary. In our previous work, we have shown that the solution of generalized (higher genus) Kashiwara-Vergne equations for an automorphism $F \\in {\\rm Aut}(L)$ of a free Lie algebra implies an isomorphism between the Goldman-Turaev Lie bialgebra $\\mathfrak{g}(\\Sigma)$ and its associated graded ${\\rm gr}\\, \\mathfrak{g}(\\Sigma)$. In this paper, we prove the converse: if $F$ induces an isomorphism $\\mathfrak{g}(\\Sigma) \\cong {\\rm gr} \\, \\mathfrak{g}(\\Sigma)$, then it satisfies the Kashiwara-Vergne equations up to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01159","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"}