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

Ethan Berkove (1) , Grant S Lakeland (2) , Alexander D. Rahm (3) , Anh Tuan Bui , Sebastian Schönnenbeck (4)

1 Mathematics Department, Lafayette College
2 Department of Mathematics, Eastern Illinois University
3 GAATI - Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information
4 Lehrstuhl II für Mathematik

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 Berkove, Grant S Lakeland, Alexander D. Rahm, Anh Tuan Bui, Sebastian Schönnenbeck. The mod 2 cohomology rings of congruence subgroups in the Bianchi groups. Journal of Algebraic Combinatorics, 2019, ⟨10.1007/s10801-019-00912-8⟩. ⟨hal-01565065v3⟩