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.
Satoh; On the Johnson filtration of the basis-conjugating a utomorphism group of a free group, Michigan Mathematical Journal, 61 (2012), 87-105
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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.