Weighted L2–cohomology of Coxeter groups based on barycentric subdivisons

Okun, Boris¹

¹ Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201, USA

Geometry & topology, Tome 8 (2004) no. 3, pp. 1032-1042.

Résumé

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 $L_q^2$–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.

Détail

DOI : 10.2140/gt.2004.8.1032

Keywords: Coxeter group, aspherical manifold, barycentric subdivision, weighted $L^2$–cohomology, Tomei manifold, Singer conjecture

Bibliographie

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