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Le delta-barre pour certains feuilletages complexes

Abstract : Leafwise Dolbeault cohomology measures the obstruction to solve the -problem along the leaves of a complex foliation. We compute this cohomology using essentially methods of cohomology of groups for some interesting examples : 1) a complex one dimensional linear foliation on the torus Tⁿ ; 2) a submersion whose fibres are elliptic curves ; 3) the two dimensional complex affine Reeb foliation on the Hopf manifold S4x S1 ; 4) the complex foliation on the hyperbolic torus obtained by a locally free action of the real affine Lie group where A∈SL (n,Z) is a hyperbolic and diagonalizable matrix whose eigenvalues are positive real numbers.
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https://hal-uphf.archives-ouvertes.fr/tel-03009673
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Jihène Slimène. Le delta-barre pour certains feuilletages complexes. Mathématiques [math]. Université de Valenciennes et du Hainaut-Cambrésis; Université de Monastir, 2008. Français. ⟨NNT : 2008VALE0012⟩. ⟨tel-03009673⟩

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