Coxeter群基于重心子的加权L^2-上同调
Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons
摘要：
任何有限旗复形L都有一个直角Coxeter群W_L和一个可收缩的三次复形Sigma_L（Davis复形），W_L作用于该复形上，且使其上的每个顶点的链环为L。由此推论，如果L是广义同调球面，则Sigma_L是可收缩的同调流形.在偶数维直角Coxeter群的重心重分剖分基础上，证明了Singer猜想的一个推广版本（关于中维以上约化加权L^2_q-上同调为零）.我们还证明了这个猜想的基础上的重心重分的单形的边界复形的细分群。
英文摘要：
Associated to any finite flag complex L there is a right-angled Coxeter group W_L and a contractible cubical complex Sigma_L (the Davis complex) 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 generalized homology sphere, then Sigma_L is a contractible homology manifold. We prove a generalized version of the Singer Conjecture (on the vanishing of the reduced weighted L^2_q-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.
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