Given a Coxeter system , there is an associated CW–complex, denoted (or simply ), on which acts properly and cocompactly. This is the Davis complex. The nerve of is a finite simplicial complex. When is a triangulation of , is a contractible –manifold. We prove that when is an even Coxeter system and is a flag triangulation of , then the reduced –homology of vanishes in all but the middle dimension.
"The $\ell^2$–homology of even Coxeter groups." Algebr. Geom. Topol. 9 (2) 1089 - 1104, 2009. https://doi.org/10.2140/agt.2009.9.1089