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De Rham cohomology of configuration spaces with Poisson measure

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JournalJournal of Functional Analysis
DatePublished - Feb 2002
Issue number1
Volume185
Number of pages33
Pages (from-to)240-273
Original languageEnglish

Abstract

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

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