Growth of regulators in finite abelian coverings

TL;DR

This paper demonstrates that the regulator in finite abelian coverings of a fixed complex grows at a sub-exponential rate, linking homology torsion and Ray-Singer torsion.

Contribution

It establishes a new growth rate bound for regulators in finite abelian coverings, connecting algebraic and analytic torsion invariants.

Findings

Regulator growth is sub-exponential in finite abelian coverings.

The regulator is defined as the difference between homology torsion and Ray-Singer torsion.

Provides a new understanding of torsion invariants in algebraic topology.

Abstract

We show that the regulator, which is the difference between the homology torsion and the combinatorial Ray-Singer torsion, of fnite abelian coverings of a fixed complex has sub-exponential growth rate.