On the fourth Johnson homomorphism of the automorphism group of a free group |
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Authors: | Takao Satoh |
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Institution: | Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto city 606-8502, Japan |
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Abstract: | 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. |
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