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We prove an analogue of the de Rham theorem for the extended L 2-cohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combi...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 1969
ISSN: 0022-2518
DOI: 10.1512/iumj.1970.19.19030