Given \alpha_0, \alpha_1 two cohomologous non-singular closed one-forms of a compact manifold M, are they always isotopic? The general answer is no; we construct obstructions living in the algebraic K-theory of some rings associated to the Novikov ring of the underlying cohomology class.

A similar problem for functions N\times [0,1] \to [0,1] without critical points was studied in [HW73] by Hatcher and Wagoner. We have carried part of their strategy to deal with this problem. In this talk, we will explain the di culties which appear when we try to generalise the Hatcher-Wagoner's approach for closed 1-forms, and give some detail on how the obstruction is constructed.