分野別セミナー

[講演概要]
The IA-automorphism group IA_n of the free group F_n is a normal subgroup of the automorphism group of F_n. Little is known about the GL(n,Z)-representation structure of the rational cohomology of IA_n except for the first and second cohomology. We study the image of the homomorphism between cohomology induced by the abelianization map of IA_n, which we call the Albanese cohomology of IA_n. In this talk, we obtain a subquotient representation of the Albanese cohomology of IA_n in a stable range, which is conjecturally equal to the entire Albanese cohomology of IA_n. Moreover, we study the whole structure of the stable rational cohomology of IA_n. This talk is partly based on joint work with Kazuo Habiro.