Reidemeister torsion and the K-theory of von Neumann algebras

We introduce a topological-type invariant for a cocompact properly discontinuous action of a discrete group on a Riemannian manifold generalizing classical notions of Reidemeister torsion. It takes values in the weak algebraic K-theory of the von Neumann algebra of . We give basic tools for its computation like sum and product formulas and calculate it in several cases. It encompasses, for instance, the Alexander polynomial and is related to analytic torsion.