Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class group

Abstract

The Torelli group and the Johnson kernel are important subgroups of the mapping class group of a surface. Using Johnson's homomorphisms as their free abelian quotients together with the representation theory of the symplectic groups, we will give some descriptions of cup products of rational cohomology classes of degree one obtained from the dual of Johnson's homomorphisms.