On the Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral 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).

Torsion homology growth for noncongruence subgroups of Bianchi groups

“…We will call the rank of Γ ab n minus cusp contribution as cuspidal rank. As was observed in [19], the cuspidal rank is typically 0, see also [8,20]. We tabulated the ranks in Table 1 where the first column represents the cuspidal rank and the second column corresponds to the number of primes in S in which we observed this cuspidal rank frequency.…”

“…There is significant amount of numerical evidence related to this conjecture (e.g. [8,19,20]). These works deal with congruence type arithmetic groups and nonarithmetic groups.…”