Authors construct obstructions to surjectivity of Johnson homomorphisms on basis-conjugating automorphism groups of free groups, determine the cokernels through degree four, and affirmatively resolve the Andreadakis problem in degree four.
Bachmuth, Induced automorphisms of free groups and free metabelian groups
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On the structures of the Johnson cokernels of the basis-conjugating automorphism groups of free groups
Authors construct obstructions to surjectivity of Johnson homomorphisms on basis-conjugating automorphism groups of free groups, determine the cokernels through degree four, and affirmatively resolve the Andreadakis problem in degree four.