Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons

Details Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons

2004-08-11

arxiv.org/abs/math/0408149v1

Geom. Topol. 8(2004) 1032-1042

Mathematics

Group Theory

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper28.abs.html

Scientific paper

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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