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

TL;DR

This paper proves that for certain sequences of congruence subgroups of Bianchi groups, the size of the torsion in the first homology grows exponentially, extending previous results to non-uniform lattices.

Contribution

It extends exponential homological torsion growth results from uniform to non-uniform lattices in Bianchi groups, including symmetric powers.

Findings

Exponential growth of torsion in homology for congruence subgroups

Includes standard exhaustive sequences and symmetric powers

Extends Bergeron and Venkatesh's results to non-uniform lattices

Abstract

In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl_2(C) the size of the torsion part in the first homology grows exponentially. This extends results of Bergeron and Venkatesh to a case of non-uniform lattices.