Multiplicativity of Reidemister-Franz Torsion for Even Manifolds

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.

18 pages