Abstract
Associated to any finite flag complex L there is a right-angled Coxeter group W L and a contractible cubical complex Σ L on which W L acts properly and cocompactly, and such that the link of each vertex is L. It follows that if L is a triangulation of S n−1 , then Σ L is a contractible n-manifold. We establish vanishing (in a certain range) of the reduced ℓ 2-homology of Σ L in the case where L is the barycentric subdivision of a cellulation of a manifold. In particular, we prove the Singer Conjecture (on the vanishing of the reduced ℓ 2-homology except in the middle dimension) in the case of Σ L where L is the barycentric subdivision of a cellulation of S n−1 , n=6,8.
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