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, Online first, 28 p.

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:
Online First:
DOI: 10.5802/aif.3531
Classification: 57K30,  57K14,  57M05,  57M10,  20C07,  20E26,  20F19,  20F65,  20J05
Keywords: Three-manifolds, fibrations, Alexander polynomials, Novikov homology
Sikorav, Jean-Claude 1

1 Unité de Mathématiques Pures et Appliquées UMR CNRS 5669 École normale supérieure de Lyon (France) 
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Sikorav, Jean-Claude. Fibered cohomology classes in dimension three, twisted Alexander polynomials and Novikov homology. Annales de l'Institut Fourier, Online first, 28 p.

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