Geometry & Topology
- Geom. Topol.
- Volume 8, Number 3 (2004), 1032-1042.
Weighted $L^2$–cohomology of Coxeter groups based on barycentric subdivisons
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.
Geom. Topol., Volume 8, Number 3 (2004), 1032-1042.
Received: 15 March 2004
Revised: 3 August 2004
Accepted: 11 July 2004
First available in Project Euclid: 21 December 2017
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Okun, Boris. Weighted $L^2$–cohomology of Coxeter groups based on barycentric subdivisons. Geom. Topol. 8 (2004), no. 3, 1032--1042. doi:10.2140/gt.2004.8.1032. https://projecteuclid.org/euclid.gt/1513883461