De Rham cohomology of configuration spaces with Poisson measure
  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 $X$. 
S. Albeverio, A. Daletskii, E. Lytvynov