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

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