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

Takuya Sakasai

doi:10.1017/s0305004107000564

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

Takuya Sakasai

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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.

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Takuya Sakasai. 2006-01-13. The second Johnson homomorphism and the second rational cohomology of the Johnson kernel. https://doi.org/10.1017/s0305004107000564

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