On the Integral Cohomology of Bianchi groups

Abstract

Extensive and systematic machine computations are carried out to investigate the integral cohomology of the Euclidean Bianchi groups and their congruence subgroups. The collected data give insight on several aspects, including the asymptotic behaviour of the torsion in the first homology. Along with the experimental work, some basic properties of the integral cohomology are recorded with an eye towards the liftibility issue of Hecke eigenvalue systems.