De Rham cohomology of configuration spaces with Poisson measure

S. Albeverio; A. Daletskii; E. Lytvynov

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De Rham cohomology of configuration spaces with Poisson measure

S. Albeverio·A. Daletskii·E. Lytvynov

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Abstract

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 $X$.

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BibTeX RIS

S. Albeverio, A. Daletskii, E. Lytvynov. 2006-08-14. De Rham cohomology of configuration spaces with Poisson measure. https://arxiv.org/abs/math/0608338

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