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2009 The $\ell^2$–homology of even Coxeter groups
Timothy A Schroeder
Algebr. Geom. Topol. 9(2): 1089-1104 (2009). 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 2–homology of Σ vanishes in all but the middle dimension.

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Timothy A Schroeder. "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

Information

Received: 28 August 2008; Revised: 22 April 2009; Accepted: 22 April 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1202.20044
MathSciNet: MR2511140
Digital Object Identifier: 10.2140/agt.2009.9.1089

Subjects:
Primary: 20F55
Secondary: 20J05, 57S30, 57T15, 58H10

Rights: Copyright © 2009 Mathematical Sciences Publishers

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