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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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.
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Dates et versions

hal-02353768 , version 1 (07-11-2019)
hal-02353768 , version 2 (12-11-2019)
hal-02353768 , version 3 (21-11-2019)
hal-02353768 , version 4 (31-01-2020)

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Jean-Claude Sikorav. FIBERED COHOMOLOGY CLASSES IN DIMENSION THREE, TWISTED ALEXANDER POLYNOMIALS AND NOVIKOV HOMOLOGY. 2020. ⟨hal-02353768v4⟩
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