#### Volume 12, issue 2 (2012)

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On the augmentation quotients of the IA-automorphism group of a free group

### Takao Satoh

Algebraic & Geometric Topology 12 (2012) 1239–1263
##### Abstract

We study the augmentation quotients of the IA-automorphism group of a free group and a free metabelian group. First, for any group $G$, we construct a lift of the $k$–th Johnson homomorphism of the automorphism group of $G$ to the $k$–th augmentation quotient of the IA-automorphism group of $G$. Then we study the images of these homomorphisms for the case where $G$ is a free group and a free metabelian group. As a corollary, we detect a $ℤ$–free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group.

##### Keywords
automorphism group of free groups, augmentation quotient, Johnson homomorphism
Primary: 20F28
Secondary: 16S34