On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups

TL;DR

This paper collects numerical data on torsion growth in the first homology of non-arithmetic hyperbolic tetrahedral groups, supporting conjectures about torsion and regulators in lattices of SL(2,C).

Contribution

It provides the first extensive numerical evidence supporting Bergeron and Venkatesh's conjectures on torsion homology growth in non-arithmetic hyperbolic groups.

Findings

Numerical data supports conjectures on torsion growth.

Evidence aligns with predictions for regulators in SL(2,C) lattices.

Supports broader theories on homology in hyperbolic groups.

Abstract

Numerical data concerning the growth of torsion in the first homology of non-arithmetic hyperbolic tetrahedral groups are collected. The data provide support the speculations of Bergeron and Venkatesh on the growth of torsion homology and the regulators for lattices in SL(2,C).