  The space $\Gamma_X$ of all locally finite configurations in a
  Riemannian manifold $X$ of infinite volume is considered. The deRham complex
of square-integrable differential forms over $\Gamma_X$, equipped with the
Poisson measure, and the corresponding deRham cohomology are studied. The
latter is shown to be unitarily isomorphic to a certain Hilbert tensor algebra
generated by the $L^2$-cohomology of the underlying manifold $X$.
