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The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

Published online by Cambridge University Press:  01 November 2007

TAKUYA SAKASAI
TAKUYA SAKASAI*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. email: sakasai@ms.u-tokyo.ac.jp
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Abstract

The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. In terms of the representation theory of the symplectic group, we give a complete description of cup products of two classes in the first rational cohomology of the Johnson kernel obtained by the rational dual of the second Johnson homomorphism.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 627 - 648
Copyright
Copyright © Cambridge Philosophical Society 2007

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