  Let X be a building of uniform thickness q+1. L^2-Betti numbers of X are
reinterpreted as von-Neumann dimensions of weighted L^2-cohomology of the
underlying Coxeter group. The dimension is measured with the help of the Hecke
algebra. The weight depends on the thickness q. The weighted cohomology makes
sense for all real positive values of q, and is computed for small q. If the
Davis complex of the Coxeter group is a manifold, a version of Poincare duality
allows to deduce that the L^2-cohomology of a building with large thickness is
concentrated in the top dimension.

Geometric Topology;Group Theory