Geometry & Topology, Vol. 8 (2004)
Paper no. 28, pages 1032--1042.
Weighted L^2-cohomology of Coxeter groups based on barycentric subdivisons
Boris L Okun
Abstract.
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.
Keywords.
Coxeter group, aspherical manifold, barycentric subdivision,
weighted L^2-cohomology, Tomei manifold, Singer conjecture
AMS subject classification.
Primary: 58G12.
Secondary: 20F55, 57S30, 20F32, 20J05.
DOI: 10.2140/gt.2004.8.1032
E-print: arXiv:math.GR/0408149
Submitted to GT on 15 March 2004.
(Revised 3 August 2004.)
Paper accepted 11 July 2004.
Paper published 7 August 2004.
Notes on file formats
Boris L Okun
Department of Mathematical Sciences
University of Wisconsin--Milwaukee
Milwaukee, WI 53201, USA
Email: okun@uwm.edu
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