Volume 6, issue 3 (2006)

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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

arXiv: math.GR/0512001

Abstract

For any Coxeter group W, we define a filtration of H(W;ZW) 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 Hc(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