Family of hyperbolic manifolds with exponential homology torsion growth

TL;DR

This paper constructs a family of hyperbolic manifolds exhibiting exponential growth in homology torsion, confirming the sharpness of recent theoretical bounds and advancing understanding of torsion behavior in hyperbolic geometry.

Contribution

It introduces a new family of hyperbolic manifolds with exponential homology torsion growth, demonstrating the optimality of existing bounds.

Findings

Homology torsion grows exponentially in the constructed manifolds.

The results confirm the sharpness of recent theoretical bounds.

Provides explicit examples matching the bounds.

Abstract

In this note, we construct a family of hyperbolic manifolds with exponentially growing torsion in their homology groups. This demonstrates that the recent bound on homological torsion, established by Bader, Gelander, and Sauer, is asymptotically sharp and cannot be improved.