Dolbeault cohomology for almost complex manifolds
From MaRDI portal
Publication:2232719
DOI10.1016/j.aim.2021.107970zbMath1478.32085arXiv1809.01416OpenAlexW3194348699MaRDI QIDQ2232719
Publication date: 8 October 2021
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.01416
Dolbeault cohomologyharmonic formsalmost complex manifoldsHodge theorynearly Kähler manifoldsFrölicher spectral sequence
General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Almost complex manifolds (32Q60)
Related Items
Harmonic forms on the Kodaira-Thurston manifold ⋮ Almost-complex invariants of families of six-dimensional solvmanifolds ⋮ Differential operators on almost-Hermitian manifolds and harmonic forms ⋮ Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence ⋮ Bott-Chern Laplacian on almost Hermitian manifolds ⋮ Bott-Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds ⋮ Rank of the Nijenhuis tensor on parallelizable almost complex manifolds ⋮ On the algebra generated by \(\overline{\mu}\), \(\overline{\partial}\), \(\partial\), \(\mu\) ⋮ Almost complex parallelizable manifolds: Kodaira dimension and special structures ⋮ On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms ⋮ Harmonic symmetries for Hermitian manifolds ⋮ An integral condition involving \(\overline{\partial}\)-harmonic \((0,1)\)-forms ⋮ On \(L^2\)-harmonic forms of complete almost Kähler manifold ⋮ Center of mass and Kähler structures ⋮ On the spectral sequence associated to a multicomplex ⋮ Maximally non-integrable almost complex structures: an \(h\)-principle and cohomological properties ⋮ Hodge-de Rham numbers of almost complex 4-manifolds
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Isomorphism theorems for cohomology groups of weakly 1-complete manifolds
- Generalized complex geometry
- Hodge theory on nearly Kähler manifolds
- Complex analytic coordinates in almost complex manifolds
- The decomposition of forms and cohomology of generalized complex manifolds
- An intrinsic volume functional on almost complex 6-manifolds and nearly Kähler geometry
- Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds
- Existence of holomorphic functions on almost complex manifolds
- A differential complex for Poisson manifolds
- A general description of the terms in the Frölicher spectral sequence
- Cohomology and Hodge theory on symplectic manifolds. I
- Cohomology and Hodge theory on symplectic manifolds. II
- Differential operators on almost-Hermitian manifolds and harmonic forms
- Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence
- Topological and geometric aspects of almost Kähler manifolds via harmonic theory
- On the spectral sequence associated to a multicomplex
- Nearly Kähler manifolds
- Théorie de Hodge. II. (Hodge theory. II)
- The Frölicher spectral sequence for compact nilmanifolds
- Some problems on differentiable and complex manifolds
- On the cohomology of compact homogeneous spaces of nilpotent Lie groups
- Dolbeault cohomology of nilmanifolds with left-invariant complex structure
- On cohomological decomposability of almost–Kähler structures
- On non-pure forms on almost complex manifolds
- Lie-algebra Dolbeault-cohomology and small deformations of nilmanifolds
- Computations of generalized Dolbeault cohomology
- Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
- Generalized Calabi-Yau Manifolds
- ON THE J-ANTI-INVARIANT COHOMOLOGY OF ALMOST COMPLEX 4-MANIFOLDS
- Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
- Harmonic symmetries for Hermitian manifolds
- RELATIONS BETWEEN THE COHOMOLOGY GROUPS OF DOLBEAULT AND TOPOLOGICAL INVARIANTS
- Dolbeault cohomology of compact nilmanifolds
