Analytic, Reidemeister and homological torsion for congruence three--manifolds

TL;DR

This paper proves that for Bianchi groups, the torsion in the first homology of congruence subgroups grows exponentially with the index, and establishes limit multiplicity results for cuspidal forms.

Contribution

It provides explicit growth rates for torsion in homology and new limit multiplicity results for cuspidal forms in the context of Bianchi groups.

Findings

Torsion in homology grows exponentially with subgroup index

Explicit growth rate for torsion established

Limit multiplicity results for cuspidal forms proved

Abstract

Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the size of the torsion subgroup of the first homology grows exponentially with the index (we give an explicit rate). We also prove limit multiplicity results for the irreducible components of the space of cuspidal forms.