Geodesic
The ℓ2–homology of even Coxeter groups
Schroeder, Timothy A1
1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 1089-1104

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2009.9.1089
Keywords: Coxeter group, $\ell ^2$-homology, Singer Conjecture, Davis complex, aspherical manifold

Schroeder, Timothy A 1

1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA 
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Schroeder, Timothy A. The ℓ2–homology of even Coxeter groups. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 1089-1104. doi: 10.2140/agt.2009.9.1089

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