no. 1
Fibered cohomology classes in dimension three, twisted Alexander polynomials and Novikov homology
Sikorav, Jean-Claude1
1 Unité de Mathématiques Pures et Appliquées UMR CNRS 5669 École normale supérieure de Lyon (France)
Annales de l'Institut Fourier, Volume 73 (2023) no. 1, pp. 279-306.

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

Nous prouvons que pour « la plupart » des variétés fermées de dimension trois, l’existence d’une forme fermée non singulière dans une classe de cohomologie donnée u∈H 1 (M,ℝ)=Hom(π 1 (M),ℝ) équivaut au fait que tout polynôme d’Alexander tordu Δ H (M,u)∈ℤ[G/keru] associé à un sous-groupe distingué d’indice fini H<π 1 (M) a un terme u-minimal unitaire.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3531
Classification: 57K30, 57K14, 57M05, 57M10, 20C07, 20E26, 20F19, 20F65, 20J05
Keywords: Three-manifolds, fibrations, Alexander polynomials, Novikov homology
Mots-clés : Variétés de dimension trois, polynômes d’Alexander, homologie de Novikov

Sikorav, Jean-Claude 1

1 Unité de Mathématiques Pures et Appliquées UMR CNRS 5669 École normale supérieure de Lyon (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Sikorav, Jean-Claude. Fibered cohomology classes in dimension three, twisted Alexander polynomials and Novikov homology. Annales de l'Institut Fourier, Volume 73 (2023) no. 1, pp. 279-306. doi : 10.5802/aif.3531. https://aif.centre-mersenne.org/articles/10.5802/aif.3531/

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