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.
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Contributor : Jean-Claude Sikorav <>
Submitted on : Tuesday, November 12, 2019 - 7:35:08 PM
Last modification on : Tuesday, November 19, 2019 - 2:11:24 AM

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  • HAL Id : hal-02353768, version 2
  • ARXIV : 1911.03251

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Jean-Claude Sikorav. FIBERED COHOMOLOGY CLASSES IN DIMENSION THREE, TWISTED ALEXANDER POLYNOMIALS AND NOVIKOV HOMOLOGY. 2019. ⟨hal-02353768v2⟩

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