  The Johnson filtration of the automorphism group of a free group is composed
of those automorphisms which act trivially on nilpotent quotients of the free
group. We compute cohomology classes as follows: (i) we analyze analogous
classes for a subgroup of the pure symmetric automorphism group of a free
group, and (ii) we analyze features of these classes which are preserved by the
Johnson homomorphism. One consequence is that the ranks of the cohomology
groups in any fixed dimension between 1 and n-1 increase without bound for
terms deep in the Johnson filtraton.
