The mapping class group invariants of the truncated group ring

We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This provides the first group cohomology computation for the mapping class group with non-symplectic coefficients since Kawazumi-Soulié. Our computation is valid in a range growing with the genus.