On the fourth Johnson homomorphism of the automorphism group of a free group

In this paper we consider the Johnson homomorphism of the automorphism group of a free group with respect to the lower central series of the IA-automorphism group of a free group. In particular, we determine the rational cokernel of the fourth Johnson homomorphism, and show that there appears a new obstruction for the surjectivity of the Johnson homomorphism. Furthermore we characterize this obstruction using trace maps.