Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groups

Abstract

In this paper we prove that for suitable sequences of subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of $$\mathrm{SL }_2(\mathbb {C})$$ the size of the torsion part in the first integral homology grows exponentially. This extends results of Bergeron and Venkatesh to a case of non-uniform lattices. Our approach is geometric. For odd symmetric powers we obtain a modified statement.