Article Dans Une Revue Revista Matemática Iberoamericana Année : 2024

Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology

Résumé

We define a transverse Dolbeault cohomology associated to any almost complex structure j on a smooth manifold M . This we do by extending the notion of transverse complex structure and by introducing a natural j-stable involutive limit distribution with such a transverse complex structure. We relate this transverse Dolbeault cohomology to the generalized Dolbeault cohomology of (M, j) introduced by Cirici and Wilson in [3], showing that the (p, 0) cohomology spaces coincide. This study of transversality leads us to suggest a notion of minimally non-integrable almost complex structure.
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hal-04920064 , version 1 (29-01-2025)

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  • HAL Id : hal-04920064 , version 1

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Michel Cahen, Jean Gutt, Simone Gutt. Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology. Revista Matemática Iberoamericana, 2024, 40 (4). ⟨hal-04920064⟩
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