Algebraic & Geometric Topology 9 (2009) 1089–1104

DOI: 10.2140/agt.2009.9.1089

Abstract

Given a Coxeter system (W,S), there is an associated CW–complex, denoted Σ(W,S) (or simply Σ), on which W acts properly and cocompactly. This is the Davis complex. The nerve L of (W,S) is a finite simplicial complex. When L is a triangulation of S³, Σ is a contractible 4–manifold. We prove that when (W,S) is an even Coxeter system and L is a flag triangulation of S³, then the reduced ℓ²–homology of Σ vanishes in all but the middle dimension.

Keywords

Coxeter group, l ²-homology, Singer Conjecture, Davis complex, aspherical manifold

Mathematical Subject Classification

Primary: 20F55

Secondary: 20J05, 57S30, 57T15, 58H10

References

Publication

Received: 28 August 2008
Revised: 22 April 2009
Accepted: 22 April 2009
Published: 26 May 2009

Authors