Colloquium on the Geometry of Groups and Numbers

Taking place at Université Pierre et Marie Curie, 8th of June, 2017.

Hans-Werner Henn (Université de Strasbourg)

On the mod-2 cohomology of SL_3(Z[1/2,i])

Let Gamma = SL_3(Z[1/2,i]), let X be any mod-2 acyclic Gamma-CW complex on which Gamma acts with finite stabilizers, e.g. the product of the symmetric space for SL(3,Z[i]) and the Bruhat-Tits building for SL_3(Q_2[i]), and let X_s be the 2-singular locus of X. We explain how to calculate the mod-2 cohomology of the Borel construction of X_s with respect to the action of Gamma. This cohomology coincides with the mod-2 cohomology of Gamma 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*(Gamma; Z/2).

Back to the colloquium on the Geometry of Groups and Numbers