A multiplicative gluing formula Reidemeister-Franz torsion of high dimensional closed manifolds

Let M be a 2n-dimensional (n≥2), closed, oriented, smooth manifold which is obtained by a connected sum of two closed, oriented, smooth manifolds and . Milnor shows that Reidemeister-Franz torsion acts multiplicatively with respect to such gluings. Namely, the torsion of M is the product of the torsions of , and the torsion of (2n-1)-sphere times a corrective term T(H*) coming from homologies. In this work, by using homological algebra techniques, we obtain a multiplicative gluing formula for the Reidemeister-Franz torsion of M with untwisted ℝ-coefficients so that the corrective term T(H*) becomes 1. Moreover, considering a connected sum decomposition for any 2ndimensional, closed, oriented, smooth manifold W, we develop a useful formula, without a corrective term, to compute the Reidemeister-Franz torsion of W with untwisted ℝ-coefficients in terms of the Reidemeister-Franz torsions of its building blocks in the decomposition.