The second Johnson homomorphism and the second rational cohomology of the Johnson kernel
arXiv:math/0601314 · doi:10.1017/S0305004107000564
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.
24 pages. An insufficient point in the original argument given in Section 4.2 is corrected by the referee's comment. To appear in Math. Proc. Cambridge Philos. Soc