Theℓ2–homology of even Coxeter groups

Timothy A Schroeder
2009 Algebraic and Geometric Topology  
Given a Coxeter system (W,S), there is an associated CW-complex, Sigma, on which W acts properly and cocompactly. We prove that when the nerve L of (W,S) is a flag triangulation of the 3-sphere, then the reduced ℓ^2-homology of Sigma vanishes in all but the middle dimension.
doi:10.2140/agt.2009.9.1089 fatcat:ev72lmfi2jhh7aztfgstzqg6qy