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2021-11-19

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cc-by (c) Cirici, Joana et al., 2021
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/181976

Dolbeault cohomology for almost complex manifolds

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https://doi.org/10.1016/j.aim.2021.107970

Abstract

This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the Dolbeault cohomology, and develop a harmonic theory which injects into Dolbeault cohomology. Lie-theoretic analogues of the theory are developed which yield important calculational tools for Lie groups and nilmanifolds. Finally, we study applications to maximally non-integrable manifolds, including nearly Kähler

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Varietats complexes, Geometria diferencial global, Homologia

Subject (English)

Complex manifolds, Global differential geometry, Homology

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CIRICI, Joana and WILSON, Scott O. Dolbeault cohomology for almost complex manifolds. Advances in Mathematics. 2021. Vol. 391. ISSN 0001-8708. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/181976

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