On the Whitehead group of Novikov rings associated to irrational homomorphisms

Given a homomorphism ξ:G→Rξ:G→R we show that the natural map i∗:Wh(G)→Wh(G;ξ) from the Whitehead group of GG to the Whitehead group of the Novikov ring is surjective. The group Wh(G;ξ) 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 ξ∈H1(M;R)ξ∈H1(M;R), where MM is a closed connected smooth manifold.