  Combinatorial aspects of the Torelli-Johnson-Morita theory of surface
automorphisms are extended to certain subgroups of the mapping class groups.
These subgroups are defined relative to a specified homomorphism from the
fundamental group of the surface onto an arbitrary group $K$. For $K$ abelian,
there is a combinatorial theory akin to the classical case, for example,
providing an explicit cocycle representing the first Johnson homomophism with
target $\Lambda ^3 K$. Furthermore, the Earle class with coefficients in $K$ is
represented by an explicit cocyle.
