Torsion homology of Bianchi Groups and Arithmetic manifolds
Mehmet Haluk Sengun (University of Warwick / ICERM)
ABSTRACT:
Bianchi groups are groups of the form SL(2,R) where R is the ring of
integers of an imaginary quadratic field. They form an important class
of arithmetic Kleinian groups and moreover they hold a key role for
the development of the Langlands program for GL(2) beyond totally real
fields.
In this talk, I will discuss several interesting questions related to
the torsion in the homology of Bianchi groups. After discussing the
importance of torsion from the perspective of number theory, I will
talk on the recent results on the asymptotic behavior of the size of
torsion. Joint work with N.Bergeron and A.Venkatesh on the cycle
complexity of arithmetic manifolds will be discussed at the end.