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2016 The fattened Davis complex and weighted $L^2$–(co)homology of Coxeter groups
Wiktor Mogilski
Algebr. Geom. Topol. 16(4): 2067-2105 (2016). DOI: 10.2140/agt.2016.16.2067


This article consists of two parts. First, we propose a program to compute the weighted L2–(co)homology of the Davis complex by considering a thickened version of this complex. The program proves especially successful provided that the weighted L2–(co)homology of certain infinite special subgroups of the corresponding Coxeter group vanishes in low dimensions. We then use our complex to perform computations for many examples of Coxeter groups. Second, we prove the weighted Singer conjecture for Coxeter groups in dimension three under the assumption that the nerve of the Coxeter group is not dual to a hyperbolic simplex, and in dimension four under the assumption that the nerve is a flag complex. We then prove a general version of the conjecture in dimension four where the nerve of the Coxeter group is assumed to be a flag triangulation of a 3–manifold.


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Wiktor Mogilski. "The fattened Davis complex and weighted $L^2$–(co)homology of Coxeter groups." Algebr. Geom. Topol. 16 (4) 2067 - 2105, 2016.


Received: 24 March 2015; Revised: 27 October 2015; Accepted: 12 November 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 06627569
MathSciNet: MR3546459
Digital Object Identifier: 10.2140/agt.2016.16.2067

Primary: 20F55
Secondary: 20F65 , 46L10 , 53C23 , 57M07 , 58J22

Keywords: Coxeter groups , fattened Davis complex , Singer conjecture , weighted L^2 cohomology

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 4 • 2016
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