Family of hyperbolic manifolds with exponential homology torsion growth

2025/12/09 by Alexandrov, Stepan
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.2512.08915

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

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.

Citations

• Homology and homotopy complexity in negative curvature
• The asymptotic growth of torsion homology for arithmetic groups

Related

• Counting non-commensurable hyperbolic manifolds and a bound on homological torsion
• Growth of homology torsion in finite coverings and hyperbolic volume
• The asymptotic growth of torsion homology for arithmetic groups
• Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
• Homology growth of polynomially growing mapping tori