A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

DOI10.4171/160-1/6zbMath1344.30042arXiv1204.0876OpenAlexW2487477593MaRDI QIDQ5740767

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/1204.0876

zbMATH Keywords

mapping class groups Johnson homomorphisms IA-automorphism groups Magnus representations

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Teichmüller theory for Riemann surfaces (30F60)

Related Items (24)

\(p\)-Johnson homomorphisms and pro-\(p\) groups ⋮ On the Universal SL₂-Representation Rings of Free Groups ⋮ ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON SPACES OF JACOBI DIAGRAMS. II ⋮ On the basis-conjugating automorphism groups of free groups and free metabelian groups ⋮ On the rings of Fricke characters of free abelian groups ⋮ Morita’s trace maps on the group of homology cobordisms ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ On the graded quotients of the \(\operatorname{SL}_m\)-representation algebras of groups ⋮ Generators and relations of ``lower-triangular automorphism groups of free groups ⋮ The third subgroup of the Andreadakis-Johnson filtration of the automorphism group of a free group ⋮ On the Andreadakis conjecture restricted to the “lower-triangular” automorphism groups of free groups ⋮ Representation stability for filtrations of Torelli groups ⋮ Generalized Johnson homomorphisms for extended N-series ⋮ Generalized Dehn twists on surfaces and homology cylinders ⋮ A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces ⋮ Meta-nilpotent quotients of mapping-torus groups and two topological invariants of quadratic forms ⋮ A Birman exact sequence for the Torelli subgroup of Aut(Fn) ⋮ Pointed harmonic volume and its relation to the extended Johnson homomorphism ⋮ On the SL(2, C)-representation rings of free abelian groups ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces ⋮ On the stable Andreadakis problem ⋮ On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three ⋮ An algebraic characterization of the point-pushing subgroup ⋮ On the graded quotients of the rings of Fricke characters of free groups.

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