The Goldman–Turaev Lie bialgebra and the Johnson homomorphisms

DOI10.4171/160-1/5zbMath1344.30038arXiv1304.1885OpenAlexW1760051519MaRDI QIDQ5740766

Yusuke Kuno, Nariya Kawazumi

Publication date: 20 July 2016

Published in: Handbook of Teichmüller Theory, Volume V (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.1885

zbMATH Keywords

Dehn twistJohnson homomorphismTorelli groupsGoldman-Turaev Lie bialgebra

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Lie bialgebras; Lie coalgebras (17B62) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (9)

The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem ⋮ Hodge theory of the Goldman bracket ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ Higher genus Kashiwara-Vergne problems and the Goldman-Turaev Lie bialgebra ⋮ Generalized Dehn twists on surfaces and homology cylinders ⋮ A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces ⋮ Goldman-Turaev formality implies Kashiwara-Vergne ⋮ Pointed harmonic volume and its relation to the extended Johnson homomorphism ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces

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