Cohomology of Coxeter groups with group ring coefficients: II

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 $\mathcal{U}$ is a CW complex on which $W$ acts as a reflection group we compute the associated graded terms for $H_{\ast }\left(\mathcal{U}\right)$ and, in the case where the action is proper and cocompact, for $H_c^{\ast }\left(\mathcal{U}\right)$.