The mod 2 cohomology rings of SL_2 of the imaginary quadratic integers

Ethan Berkove (1) , Alexander D. Rahm (2)

1 Mathematics Department, Lafayette College
2 NUIG - Department of Mathematics

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.

Mots clés: Cohomology of arithmetic groups

Domaines: K-théorie et homologie [math.KT]

Ethan Berkove, Alexander D. Rahm. The mod 2 cohomology rings of SL_2 of the imaginary quadratic integers. 2014. ⟨hal-00769261v3⟩