Let W be a compact oriented Riemannian manifold of dimension N, and let K be a simplicial complex which is a smooth triangulation of W. The Reidemeister-Franz torsion (or R-torsion) 7 of K is a function of certain representations of the fundamental group of K. Since it is a combinatorial invariant, and since smooth triangulations of W are equivalent, this torsion is a manifold invariant. We raise the question as to how to describe this manifold invariant in analytic terms. Arnold Shapiro onceâ€¦Â CONTINUE READING