The mod 2 cohomology rings of congruence subgroups in the Bianchi groups

We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental domains, and an analysis of the equivariant spectral sequence combined with torsion subcomplex reduction.__________With an appendix by Bui Anh Tuan and Sebastian Sch{"o}nnenbeck