De Rham cohomology of configuration spaces with Poisson measure

The space ΓX of all locally finite configurations in a Riemannian manifold X of infinite volume is considered. The deRham complex of square-integrable differential forms over ΓX, 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 L2-cohomology of the underlying manifold X.