Geometry & Topology

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

Boris Okun

Full-text: Open access

Abstract

Associated to any finite flag complex L there is a right-angled Coxeter group WL and a contractible cubical complex ΣL (the Davis complex) on which WL 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 ΣL is a contractible homology manifold. We prove a generalized version of the Singer Conjecture (on the vanishing of the reduced weighted Lq2–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.

Article information

Source
Geom. Topol., Volume 8, Number 3 (2004), 1032-1042.

Dates
Received: 15 March 2004
Revised: 3 August 2004
Accepted: 11 July 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883461

Digital Object Identifier
doi:10.2140/gt.2004.8.1032

Mathematical Reviews number (MathSciNet)
MR2087077

Zentralblatt MATH identifier
1062.58026

Subjects
Primary: 58G12
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 57S30: Discontinuous groups of transformations 20F32 20J05: Homological methods in group theory

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

Citation

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


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References

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