  The Johnson filtration of the mapping class group of a compact, oriented
surface is the descending series consisting of the kernels of the actions on
the nilpotent quotients of the fundamental group of the surface. Each term of
the Johnson filtration admits a Johnson homomorphism, whose kernel is the next
term in the filtration. In this paper, we consider a general situation where a
group acts on a group with a filtration called an "extended N-series". We
develop a theory of Johnson homomorphisms in this general setting, including
many known variants of the original Johnson homomorphisms as well as several
new variants.
