De Rham theorem for extended L^2-cohomology
Abstract
Description
We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. 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 (with bounded morphisms and homotopy operators) to a combinatorial complex with the same coefficients. This is established by using the Witten deformation of the de Rham complex. We also prove that the de Rham complex is chain-homotopy equivalent to the spectrally truncated de Rham complex which is also finitely generated.
16 pages, author-supplied file available at ftp://ftp.math.neu.edu/Pub/faculty/Shubin_Mikhail/papers/DR19.tex This is a slight revision -- some references are added AMSTeX v 2.1
16 pages, author-supplied file available at ftp://ftp.math.neu.edu/Pub/faculty/Shubin_Mikhail/papers/DR19.tex This is a slight revision -- some references are added AMSTeX v 2.1