-Betti Numbers of Infinite Configuration Spaces
Sergio Albeverio
Universität Bonn, GermanyAlexei Daletskii
Nottingham Trent University, United Kingdom
![$L^2$-Betti Numbers of Infinite Configuration Spaces cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-prims-volume-42-issue-3.png&w=3840&q=90)
Abstract
The space of all locally finite configurations in a infinite covering of a compact Riemannian manifold is considered. The de Rham complex of square-integrable differential forms over , 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, -Betti Numbers of Infinite Configuration Spaces. Publ. Res. Inst. Math. Sci. 42 (2006), no. 3, pp. 649–682
DOI 10.2977/PRIMS/1166642153