The Equisymmetric Stratification of the Moduli Space and the Krull Dimension of the Mapping Class Group
A stratification of the moduli space into strata consisting of the Riemann surfaces of the same symmetry type is discussed. The stratification is then employed to determine the Krull dimension of the mod p cohomology algebras of mapping class groups.
Broughton, S.A. (1990). The equisymmetric stratification of the moduli space and the Krull dimension of the mapping class group. In Topology and its Applications, 37, 101-113.