De Rham cohomology of configuration spaces with Poisson measure

Details De Rham cohomology of configuration spaces with Poisson measure De Rham cohomology of configuration spaces with Poisson measure

2006-08-14

arxiv.org/abs/math/0608338v1

J. Funct. Anal. 185 (2001), 240-273

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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 $X$.

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