Exponential Torsion Growth for Random 3-Manifolds

TL;DR

This paper demonstrates that random 3-manifolds with positive first Betti number have a tower of cyclic covers exhibiting exponential growth in torsion, revealing new insights into their algebraic and topological properties.

Contribution

It establishes the existence of exponential torsion growth in towers of cyclic covers for a broad class of random 3-manifolds with positive first Betti number.

Findings

Exponential torsion growth occurs in cyclic covers of random 3-manifolds.

Positive first Betti number is a key condition for torsion growth.

Provides a probabilistic framework for understanding 3-manifold torsion growth.

Abstract

We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth.