On the Whitehead group of Novikov rings associated to irrational homomorphisms

Given a homomorphism image we show that the natural map image from the Whitehead group of G to the Whitehead group of the Novikov ring is surjective. The group image is of interest for the simple chain homotopy type of the Novikov complex. It also contains the Latour obstruction for the existence of a nonsingular closed 1-form within a fixed cohomology class image, where M is a closed connected smooth manifold.