On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups

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).

💡 Research Summary

The paper investigates the growth of torsion in the first homology of non‑arithmetic hyperbolic tetrahedral groups and compares the numerical findings with the conjectural framework of Bergeron and Venkatesh. Bergeron‑Venkatesh proved that for a tower of cocompact arithmetic lattices in SL(2,ℂ) with trivial torsion in the congruence subgroups, the quantity
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