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 ${H}^{\ast }\left(W;ZW\right)$ by $W$–submodules and then compute the associated graded terms. More generally, if $\mathsc{U}$ is a CW complex on which $W$ acts as a reflection group we compute the associated graded terms for ${H}_{\ast }\left(\mathsc{U}\right)$ and, in the case where the action is proper and cocompact, for ${H}_{c}^{\ast }\left(\mathsc{U}\right)$.

Keywords
Coxeter group, Hecke algebra, building, cohomology of groups
Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 20C08, 20E42, 20F65, 20J06, 57M07