Goldman-Turaev formality implies Kashiwara-Vergne

DOI10.4171/QT/143zbMath1479.57036arXiv1812.01159OpenAlexW3093996380MaRDI QIDQ2043514

Florian Naef, Anton Yu. Alekseev, Nariya Kawazumi, Yusuke Kuno

Publication date: 2 August 2021

Published in: Quantum Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.01159

zbMATH Keywords

free Lie algebrasGoldman bracketTuraev cobracketKashiwara-Vergne problem

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Lie bialgebras; Lie coalgebras (17B62) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (3)

Around Van den Bergh’s double brackets for different bimodule structures ⋮ Hamiltonian structures for integrable nonabelian difference equations ⋮ The Lie bracket of undirected closed curves on a surface

Cites Work

• Unnamed Item
• The Kashiwara-Vergne conjecture and Drinfeld's associators
• Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations
• Necklace Lie algebras and noncommutative symplectic geometry.
• Poisson brackets in Kontsevich's ``Lie World
• Noncommutative geometry and quiver algebras
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• The Campbell-Hausdorff formula and invariant hyperfunctions
• The Kontsevich integral and Milnor's invariants
• Goldman-Turaev formality from the Knizhnik-Zamolodchikov connection
• The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem
• Formal descriptions of Turaev's loop operations
• Hodge theory of the Goldman bracket
• The logarithms of Dehn twists
• Fox pairings and generalized Dehn twists
• A combinatorial construction of symplectic expansions
• Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant
• Double Poisson algebras
• Skein quantization of Poisson algebras of loops on surfaces
• The Goldman–Turaev Lie bialgebra and the Johnson homomorphisms
• Non-commutative symplectic geometry, quiver varieties, and operads
• Intersection of curves on surfaces and their applications to mapping class groups

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