Multiplicativity of Reidemister-Franz Torsion for Even Manifolds

TL;DR

This paper proves that Reidemeister-Franz torsion for certain even-dimensional manifolds decomposes multiplicatively under connected sum, revealing a fundamental property of torsion in topological manifold analysis.

Contribution

It establishes the multiplicativity of Reidemeister-Franz torsion for non-acyclic complexes on highly connected even manifolds, using unique prime factorization.

Findings

Reidemeister-Franz torsion decomposes multiplicatively for these manifolds.

Connected sum monoid admits unique prime factorization.

Torsion decomposition occurs without corrective terms.

Abstract

We study Reidemeister-Franz torsion for non-acyclic cellular chain complexes arising from closed, oriented, highly connected even dimensional manifolds. The monoid of such manifolds under connected sum admits a unique factorisation into indecomposable elements. Using this factorisation, we prove that the Reidemeister-Franz torsion of an even-dimensional manifold decomposes multiplicatively as the product of the torsions of its prime factors without any corrective term.