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Journal of the London Mathematical Society 2006 74(2):341-360; doi:10.1112/S0024610706022976
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© The London Mathematical Society 2006

NEW OBSTRUCTIONS FOR THE SURJECTIVITY OF THE JOHNSON HOMOMORPHISM OF THE AUTOMORPHISM GROUP OF A FREE GROUP

Takao Satoh

Graduate School of Mathematical Sciences, The University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo, 153-8914, Japan takao{at}ms.u-tokyo.ac.jp

Received 6 April 2005. Revision received 12 September 2005.

In this paper we construct new obstructions for the surjectivity of the Johnson homomorphism of the automorphism group of a free group. We also determine the structure of the cokernel of the Johnson homomorphism for degrees 2 and 3.


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