  Let G_0,...,G_k be finite abelian groups and let G_0*...*G_k be the join of
the 0-dimensional complexes G_i. We give a characterization of the integral
k-coboundaries of subcomplexes of G_0*...*G_k in terms of the Fourier transform
on the group G_0 \times ... \times G_k. This leads to an extension of a recent
result of Musiker and Reiner on a topological interpretation of the cyclotomic
polynomial.
