De Rham cohomology of configuration spaces with Poisson measure

英文摘要：

The space $Γ_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $Γ_X$, 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 $X$.