De Rham cohomology of configuration spaces with Poisson measure

A. Daletskii; S. Albeverio; E. Lytvynov

doi:10.1006/jfan.2001.3766

De Rham cohomology of configuration spaces with Poisson measure

A. Daletskii, S. Albeverio, E. Lytvynov

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	240-273
Number of pages	33
Journal	Journal of Functional Analysis
Volume	185
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2001.3766
Publication status	Published - Feb 2002

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10.1006/jfan.2001.3766

http://dx.doi.org/10.1006/jfan.2001.3766

Cite this

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title = "De Rham cohomology of configuration spaces with Poisson measure",

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.",

author = "A. Daletskii and S. Albeverio and E. Lytvynov",

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AU - Albeverio, S.

AU - Lytvynov, E.

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AB - 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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DO - 10.1006/jfan.2001.3766

M3 - Article

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SP - 240

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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