Appears in collection : Summer School 2024 - Low dimensional Topology

The IA-automorphism group IA_n of the free group F_n is a normal subgroup of the automorphism group of F_n, which is an analogue of the Torelli groups of surfaces. The homology of IA_n admits an action of the general linear group GL(n,Z). We study the GL(n,Z)-representation structure of the homology of IA_n for sufficiently large n. In this talk, we determine the GL(n,Z)-representation structure of the Albanese homology of IA_n, which is an important quotient of the rational homology of IA_n. We also present some by-products.