  We study the relation between Sobolev inequalities for differential forms on
a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold.
The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space
of closed differential forms in $L^p(M)$ modulo the exact forms which are
exterior differentials of forms in $L^q(M)$.
