  We present a family of complexes playing the same role, for homogeneous
variational problems, that the horizontal parts of the variational bicomplex
play for variational problems on a fibred manifold. We show that, modulo
certain pullbacks, each of these complexes (apart from the first one) is
globally exact. All the complexes may be embedded in bicomplexes, and we show
that, again modulo pullbacks, the latter are locally exact. The edge sequence
is an important part of such a bicomplex, and may be used for the study of
homogeneous variational problems.
