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

Ethan S Berkove (1) , Grant S Lakeland (2) , Alexander D. Rahm (3)

1 Mathematics Department, Lafayette College
2 Department of Mathematics, Eastern Illinois University
3 FSTC - Faculty of Science, Technology and Communication [Luxembourg]

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 Schönnenbeck

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

Ethan S Berkove, Grant S Lakeland, Alexander D. Rahm. The mod 2 cohomology rings of congruence subgroups in the Bianchi groups. 2017. ⟨hal-01565065v1⟩