On torsion of non-acyclic cellular chain complexes of even manifolds in a unique factorisation monoid

Abstract: Let $\mathcal{M}{2n}^{\mathrm{Diff},\mathrm{hc}}$ be a multiplicative factorisation monoid over highly connected differentiable closed connected oriented manifolds. Any $2n$-dimensional manifold $W_p^{2n}$ from $\mathcal{M}{2n}^{\mathrm{Diff},\mathrm{hc}}$ admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. By using this decomposition, we prove that Reidemeister-Franz torsion of $W_p^{2n}$ can be written as the product of Reidemeister-Franz torsions of the manifolds in the decomposition without the corrective term.