FIBERED COHOMOLOGY CLASSES IN DIMENSION THREE, TWISTED ALEXANDER POLYNOMIALS AND NOVIKOV HOMOLOGY

Abstract

We prove that for "most" closed 3-dimensional manifolds N , the existence of a closed non singular one-form in a given cohomology class u ∈ H 1 (M, R) is equivalent to the non-vanishing modulo p of all twisted Alexander polynomials associated to finite Galois coverings of N. When u ∈ H 1(M,Z), a stronger version of this had been proved by S. Friedl and S. Vidussi in 2013, asking only the non-vanishing of the Alexander polynomials