The logarithms of Dehn twists

DOI10.4171/QT/54zbMath1361.57027arXiv1008.5017OpenAlexW2963665518MaRDI QIDQ2259627

Yusuke Kuno, Nariya Kawazumi

Publication date: 5 March 2015

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

Full work available at URL: https://arxiv.org/abs/1008.5017

zbMATH Keywords

mapping class groupDehn twistsJohnson homomorphismsGoldman Lie algebra

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Algebraic topology on manifolds and differential topology (57R19)

Related Items (18)

Hodge theory of the Turaev cobracket and the Kashiwara-Vergne problem ⋮ Johnson homomorphisms ⋮ The Torelli group and the Kauffman bracket skein module ⋮ Triviality of the 𝐽₄-equivalence among homology 3-spheres ⋮ The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem ⋮ Quasi-Lie bialgebras of loops in quasisurfaces ⋮ Hodge theory of the Goldman bracket ⋮ Topological constructions of tensor fields on moduli spaces ⋮ The geometric intersection number of simple closed curves on a surface and symplectic expansions of free groups ⋮ Fox pairings and generalized Dehn twists ⋮ Generalized Dehn twists on surfaces and homology cylinders ⋮ Intersection of curves on surfaces and their applications to mapping class groups ⋮ Goldman-Turaev formality implies Kashiwara-Vergne ⋮ Pointed harmonic volume and its relation to the extended Johnson homomorphism ⋮ Poisson brackets in Kontsevich's ``Lie World ⋮ Quasi-Poisson structures on moduli spaces of quasi-surfaces ⋮ Loops in surfaces and star-fillings ⋮ The quotient of a Kauffman bracket skein algebra by the square of an augmentation ideal

Cites Work

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• Canonical extensions of the Johnson homomorphisms to the Torelli groupoid
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• Extension of \(C^\infty\) function algebra by integrals and Malcev completion of \(\pi_1\)
• Extending Johnson's and Morita's homomorphisms to the mapping class group
• EXTENSIONS OF JOHNSON'S AND MORITA'S HOMOMORPHISMS THAT MAP TO FINITELY GENERATED ABELIAN GROUPS

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