The ℓ2–homology of even Coxeter groups

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 $S^{3}$ , $Σ$ is a contractible $4$ –manifold. We prove that when $(W, S)$ is an even Coxeter system and $L$ is a flag triangulation of $S^{3}$ , then the reduced $ℓ^{2}$ –homology of $Σ$ vanishes in all but the middle dimension.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

Keywords

Coxeter group, $\ell ^2$-homology, Singer Conjecture, Davis complex, aspherical manifold

Mathematical Subject Classification 2000

Primary: 20F55

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

References

Publication

Received: 28 August 2008

Revised: 22 April 2009

Accepted: 22 April 2009

Published: 26 May 2009

Authors

Timothy A Schroeder
Department of Mathematics and Statistics Murray State University Murray, KY 42071 USA

Volume 9, issue 2 (2009)

Timothy A Schroeder

Abstract