The ${\ell }^2$-homology of even Coxeter groups

Abstract

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 ${\ell }^2$-homology of Sigma vanishes in all but the middle dimension.

15 pages, 1 figure

References in corpus (1)

• Weighted $L^2$-cohomology of Coxeter groups

Cited by in corpus (4)

• The $L^2$-(co)homology of groups with hierarchies
• The weighted Singer conjecture for Coxeter groups in dimensions three and four
• On the three-dimensional Singer Conjecture for Coxeter groups
• Statements and Dilemmas Regarding the ${\ell }^2$-homology of Coxeter groups