Permutations in tensor products of factors, and L^2 cohomology of configuration spaces - Kalyuzhnyi, A. A.; Daletskii, A. (Methods of Functional Analysis and Topology, 2006)
We prove that the natural action of permutations in a tensor product of type II factors is free, and compute the von Neumann trace of the projection onto the space of symmetric and antisymmetric elements respectively. We apply this result to computation of von Neumann dimensions of the spaces of square-integrable harmonic forms (L^2-Betti numbers) of N-point configurations in Riemannian manifolds with infinite discrete groups of isometries.