Abstract
Associated to any finite flag complex there is a right-angled Coxeter group and a contractible cubical complex (the Davis complex) on which acts properly and cocompactly, and such that the link of each vertex is . It follows that if is a generalized homology sphere, then is a contractible homology manifold. We prove a generalized version of the Singer Conjecture (on the vanishing of the reduced weighted –cohomology above the middle dimension) for the right-angled Coxeter groups based on barycentric subdivisions in even dimensions. We also prove this conjecture for the groups based on the barycentric subdivision of the boundary complex of a simplex.
Citation
Boris Okun. "Weighted $L^2$–cohomology of Coxeter groups based on barycentric subdivisons." Geom. Topol. 8 (3) 1032 - 1042, 2004. https://doi.org/10.2140/gt.2004.8.1032
Information