The asymptotic growth of torsion homology for arithmetic groups

TL;DR

This paper investigates the conditions under which torsion in the homology of arithmetic groups grows exponentially with their covolume, providing numerous examples and conjectures.

Contribution

It offers new insights and conjectures on the exponential growth of torsion homology in arithmetic groups, supported by multiple examples.

Findings

Identifies conditions for exponential torsion growth

Provides numerous illustrative examples

Proposes conjectures on torsion growth behavior

Abstract

When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.