JournalsprimsVol. 42, No. 3pp. 649–682

<em>L</em><sup>2</sup>-Betti Numbers of Infinite Configuration Spaces

  • Sergio Albeverio

    Universität Bonn, Germany
  • Alexei Daletskii

    Nottingham Trent University, United Kingdom
<em>L</em><sup>2</sup>-Betti Numbers of Infinite Configuration Spaces cover
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Abstract

The space Γ_X_ of all locally finite configurations in a infinite covering X of a compact Riemannian manifold is considered. The de Rham complex of square-integrable differential forms over Γ_X_, equipped with the Poisson measure, and the corresponding de Rham cohomology and the spaces of harmonic forms are studied. A natural von Neumann algebra containing the projection onto the space of harmonic forms is constructed. Explicit formulae for the corresponding trace are obtained. A regularized index of the Dirac operator associated with the de Rham differential on the configuration space of an infinite covering is considered.

Cite this article

Sergio Albeverio, Alexei Daletskii, <em>L</em><sup>2</sup>-Betti Numbers of Infinite Configuration Spaces. Publ. Res. Inst. Math. Sci. 42 (2006), no. 3, pp. 649–682

DOI 10.2977/PRIMS/1166642153