On the mod-2 cohomology of SL3ℤ,i

Abstract

Let Γ = SL 3 (Z[ 1 2 , i]), let X be any mod-2 acyclic Γ-CW complex on which Γ acts with finite stabilizers and let Xs be the 2-singular locus of X. We calculate the mod-2 cohomology of the Borel constructon of Xs with respect to the action of Γ. This cohomology coincides with the mod-2 cohomology of Γ in cohomological degrees bigger than 8 and the result is compatible with a conjecture of Quillen which predicts the strucure of the cohomology ring H * (Γ; Z/2).