On the three-dimensional Singer Conjecture for Coxeter groups

Timothy A. Schroeder

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arXiv · 0909.0071

On the three-dimensional Singer Conjecture for Coxeter groups

Timothy A. Schroeder

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Abstract

We give a proof of the Singer conjecture (on the vanishing of reduced $\ell^2$-homology except in the middle dimension) for the Davis Complex $Σ$ associated to a Coxeter system $(W,S)$ whose nerve $L$ is a triangulation of $\mathbb{S}^2$. We show that it follows from a theorem of Andreev, which gives the necessary and sufficient conditions for a classical reflection group to act on $\mathbb{H}^3$.

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Timothy A. Schroeder. 2009-09-01. On the three-dimensional Singer Conjecture for Coxeter groups. https://arxiv.org/abs/0909.0071

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