The decomposition of forms and cohomology of generalized complex manifolds

DOI10.1016/j.geomphys.2006.02.006zbMath1106.57019OpenAlexW2032455027MaRDI QIDQ856763

Gil R. Cavalcanti

Publication date: 7 December 2006

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2006.02.006

zbMATH Keywords

generalized complex geometrycohomology decomposition

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Differential forms in global analysis (58A10) Other complex differential geometry (53C56) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)

Related Items (18)

Polynomial structures in generalized geometry ⋮ Invariant generalized complex structures on flag manifolds ⋮ Invariant generalized complex geometry on maximal flag manifolds and their moduli ⋮ Generalized almost product structures and generalized CRF-structures ⋮ On cohomological decomposition of generalized-complex structures ⋮ Spectral action for scalar perturbations of Dirac operators ⋮ Dolbeault cohomology for almost complex manifolds ⋮ The Frölicher-type inequalities of foliations ⋮ Cohomologies of generalized complex manifolds and nilmanifolds ⋮ Hodge theory of SKT manifolds ⋮ A Frölicher-type inequality for generalized complex manifolds ⋮ On holomorphic maps and generalized complex geometry ⋮ Topology of generalized complex quotients ⋮ Invariance of basic Hodge numbers under deformations of Sasakian manifolds ⋮ The equivariant cohomology theory of twisted generalized complex manifolds ⋮ Invariant generalized almost complex structures on real flag manifolds ⋮ Invariant generalized complex structures on partial flag manifolds ⋮ Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds

Cites Work

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• Generalized complex geometry
• A differential complex for Poisson manifolds
• Real homotopy theory of Kähler manifolds
• Harmonic cohomology classes of symplectic manifolds
• Hodge structure on symplectic manifolds
• The Lefschetz property, formality and blowing up in symplectic geometry
• Generalized Calabi-Yau Manifolds
• On the Structure of Compact Complex Analytic Surfaces, I
• RELATIONS BETWEEN THE COHOMOLOGY GROUPS OF DOLBEAULT AND TOPOLOGICAL INVARIANTS

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