Algebraic & Geometric Topology

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

Takao Satoh

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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 –free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 2 (2012), 1239-1263.

Dates
Received: 4 April 2011
Revised: 22 March 2012
Accepted: 23 March 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715388

Digital Object Identifier
doi:10.2140/agt.2012.12.1239

Mathematical Reviews number (MathSciNet)
MR2928912

Zentralblatt MATH identifier
1261.20036

Subjects
Primary: 20F28: Automorphism groups of groups [See also 20E36]
Secondary: 16S34: Group rings [See also 20C05, 20C07], Laurent polynomial rings

Keywords
automorphism group of free groups augmentation quotient Johnson homomorphism

Citation

Satoh, Takao. On the augmentation quotients of the IA-automorphism group of a free group. Algebr. Geom. Topol. 12 (2012), no. 2, 1239--1263. doi:10.2140/agt.2012.12.1239. https://projecteuclid.org/euclid.agt/1513715388


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