{"paper":{"title":"The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Anton Alekseev, Florian Naef, Nariya Kawazumi, Yusuke Kuno","submitted_at":"2017-03-16T20:47:38Z","abstract_excerpt":"In this paper, we describe a surprising link between the theory of the Goldman-Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara-Vergne (KV) problem in Lie theory. Let $\\Sigma$ be an oriented 2-dimensional manifold with non-empty boundary and $\\mathbb{K}$ a field of characteristic zero. The Goldman-Turaev Lie bialgebra is defined by the Goldman bracket $\\{ -,- \\}$ and Turaev cobracket $\\delta$ on the $\\mathbb{K}$-span of homotopy classes of free loops on $\\Sigma$.\n  Applying an expansion $\\theta: \\mathbb{K}\\pi \\to \\mathbb{K}\\langle x_1, \\dots, x_n \\rangle$ yields an algebraic de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05813","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"}