De Rham cohomology of configuration spaces with Poisson measure

S. Albeverio; A. Daletskii; E. Lytvynov

De Rham cohomology of configuration spaces with Poisson measure

Probability 2016-09-07 v1 Mathematical Physics math.MP

Authors: S. Albeverio , A. Daletskii , E. Lytvynov

Abstract

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 $X$ .

Keywords

configuration space poisson measure de rham cohomology square-integrable forms riemannian manifold hilbert tensor algebra unitary isomorphism

Cite

@article{arxiv.math/0608338,
  title  = {De Rham cohomology of configuration spaces with Poisson measure},
  author = {S. Albeverio and A. Daletskii and E. Lytvynov},
  journal= {arXiv preprint arXiv:math/0608338},
  year   = {2016}
}

De Rham cohomology of configuration spaces with Poisson measure

Abstract

Keywords

Cite

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