NEW OBSTRUCTIONS FOR THE SURJECTIVITY OF THE JOHNSON HOMOMORPHISM OF THE AUTOMORPHISM GROUP OF A FREE GROUP

DOI10.1112/S0024610706022976zbMath1118.20037OpenAlexW2121161408MaRDI QIDQ3419078

Takao Satoh

Publication date: 6 February 2007

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0024610706022976

zbMATH Keywords

graded Lie algebrasranksgroups of automorphismsfree groupslower central seriesJohnson homomorphismsIA-automorphisms

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Automorphism groups of groups (20F28) Free nonabelian groups (20E05) Derived series, central series, and generalizations for groups (20F14) Associated Lie structures for groups (20F40)

Related Items (19)

On the image of the Burau representation of the IA-automorphism group of a free group. ⋮ On the Johnson filtration of the basis-conjugating automorphism group of a free group. ⋮ On the lower central series of the IA-automorphism group of a free group. ⋮ On the basis-conjugating automorphism groups of free groups and free metabelian groups ⋮ First cohomologies and the Johnson homomorphisms of the automorphism group of a free group. ⋮ On the augmentation quotients of the IA-automorphism group of a free group. ⋮ On the derivation algebra of the free Lie algebra and trace maps ⋮ The Johnson filtration of the McCool stabilizer subgroup of the automorphism group of a free group ⋮ On the graded quotients of the \(\operatorname{SL}_m\)-representation algebras of groups ⋮ The third subgroup of the Andreadakis-Johnson filtration of the automorphism group of a free group ⋮ EXTENSIONS OF JOHNSON'S AND MORITA'S HOMOMORPHISMS THAT MAP TO FINITELY GENERATED ABELIAN GROUPS ⋮ On the Andreadakis conjecture restricted to the “lower-triangular” automorphism groups of free groups ⋮ On the Andreadakis-Johnson filtration of the automorphism group of a free group. ⋮ On the fourth Johnson homomorphism of the automorphism group of a free group. ⋮ The cokernel of the Johnson homomorphisms of the automorphism group of a free metabelian group ⋮ A reduction of the target of the Johnson homomorphisms of the automorphism group of a free group ⋮ The kernel of the Magnus representation of the automorphism group of a free group is not finitely generated ⋮ On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three ⋮ The Johnson homomorphism and the second cohomology of \(\text{IA}_n\).

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