Abstract
We study the augmentation quotients of the IA-automorphism group of a free group and a free metabelian group. First, for any group , we construct a lift of the –th Johnson homomorphism of the automorphism group of to the –th augmentation quotient of the IA-automorphism group of . Then we study the images of these homomorphisms for the case where is a free group and a free metabelian group. As a corollary, we detect a –free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group.
Citation
Takao Satoh. "On the augmentation quotients of the IA-automorphism group of a free group." Algebr. Geom. Topol. 12 (2) 1239 - 1263, 2012. https://doi.org/10.2140/agt.2012.12.1239
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