Fibered cohomology classes in dimension three, twisted Alexander polynomials and Novikov homology

We prove that for “most” closed 3-dimensional manifolds M, the existence of a non singular one-form in given cohomology class u∈H 1 (M,ℝ)=Hom(π (M),ℝ) is equivalent to fact every twisted Alexander polynomial Δ H (M,u)∈ℤ[G/keru] associated normal subgroup with finite index H<π (M) has unitary u-minimal term.