Cohomology of Coxeter groups with group ring coefficients: II

Davis, Michael W; Dymara, Jan; Januszkiewicz, Tadeusz; Okun, Boris

doi:10.2140/agt.2006.6.1289

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Cohomology of Coxeter groups with group ring coefficients: II

Michael W Davis, Jan Dymara, Tadeusz Januszkiewicz and Boris Okun

Algebraic & Geometric Topology 6 (2006) 1289–1318

DOI: 10.2140/agt.2006.6.1289

arXiv: math.GR/0512001

Abstract

For any Coxeter group $W$ , we define a filtration of $H^{*} (W; Z W)$ by $W$ –submodules and then compute the associated graded terms. More generally, if $U$ is a CW complex on which $W$ acts as a reflection group we compute the associated graded terms for $H_{*} (U)$ and, in the case where the action is proper and cocompact, for $H_{c}^{*} (U)$ .

Keywords

Coxeter group, Hecke algebra, building, cohomology of groups

Mathematical Subject Classification 2000

Primary: 20F55

Secondary: 20C08, 20E42, 20F65, 20J06, 57M07

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Publication

Received: 10 April 2006

Revised: 28 June 2006

Accepted: 22 June 2006

Published: 15 September 2006

Authors

Michael W Davis
The Ohio State University Department of Mathematics 231 W 18th Ave Columbus, Ohio 43210–1174 USA

Jan Dymara
Instytut Matematyczny, Uniwersytet Wrocławski pl. Grunwaldzki 2/4 50-384 Wrocław Poland

Tadeusz Januszkiewicz
The Ohio State University Department of Mathematics 231 W 18th Ave Columbus, Ohio 43210–1174 USA

Boris Okun
University of Wisconsin–Milwaukee Department of Mathematical Sciences PO Box 413 Milwaukee WI 53201–0413 USA

Volume 6, issue 3 (2006)