Cohomology of Bianchi Groups and Arithmetic

Bianchi groups are groups of the form SL(2,R) where R is the ring of an imaginary quadratic field.
'They arise naturally in the study of hyperbolic 3-manifolds and of certain generalizations of the classical modular forms (called Bianchi modular forms) for which they assume the role of the classical modular
group SL(2,Z).

After giving the necessary background, I will start with a  discussion of the problem of
understanding the behavior of the dimensions of the cohomology of Bianchi groups and
their congruence subgroups. 

Next, I will focus on the amount of the torsion that one encounters in the cohomology .

Finally, I will discuss the  arithmetic significance of these torsion classes.