The mod 2 cohomology rings of SL\_2 of the imaginary quadratic integers

Abstract

We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL\_2 groups over imaginary quadratic integers on their associated symmetric space. On the way, we extend the torsion subcomplex reduction technique to cases where the kernel of the group action is nontrivial. Using the equivariant and Lyndon-Hochschild-Serre spectral sequences, we investigate the second page differentials and show how to obtain the mod 2 cohomology rings of our groups from this information.

arXiv commentVersion post-print corrigeant de petits erreurs concernant l'observation qui se réfère sur l'appendice, Journal of Pure and Applied Algebra, Elsevier, 2015, Accepted for publication on July 21, 2015