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

Satoh, Takao¹

¹Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 1239-1263

Résumé

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.

Détail

DOI : 10.2140/agt.2012.12.1239

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

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