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Associated to any finite flag complex L there is a right-angled Coxeter groupW_L and a contractible cubical complex Sigma_L (the Davis complex) on which W_Lacts properly and cocompactly, and such that the link of each vertex is L. Itfollows that if L is a generalized homology sphere, then Sigma_L is acontractible homology manifold. We prove a generalized version of the SingerConjecture (on the vanishing of the reduced weighted L^2_q-cohomology above themiddle dimension) for the right-angled Coxeter groups based on barycentricsubdivisions in even dimensions. We also prove this conjecture for the groupsbased on the barycentric subdivision of the boundary complex of a simplex.

WeightedL2–cohomology of Coxeter groups based on barycentric subdivisons

WeightedL²–cohomology of Coxeter groups based on barycentric subdivisons