分野別セミナー

【講演要旨】 The IA-automorphism group IA_n of the free group F_n is a normal subgroup of the automorphism group Aut(F_n) of F_n. The rational homology of IA_n has been studied by many authors. However, to the best of our knowledge, the homology of IA_n with non-trivial coefficients has not been computed. In this talk, we consider the Aut(F_n)-module A_2(n) of Jacobi diagrams of degree 2 on n-component oriented arcs. We compute the GL(n,Z)-representation structure of the first homology of IA_n with coefficients in A_2(n).