Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
From MaRDI portal
Publication:4505927
DOI10.1090/S0002-9947-00-02486-7zbMath0965.32026OpenAlexW1871825518MaRDI QIDQ4505927
Marisa Fernández, Luis A. Cordero, Alfred Gray, Luis Ugarte
Publication date: 3 October 2000
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02486-7
Homogeneous complex manifolds (32M10) Complex manifolds (32Q99) Homology and cohomology of homogeneous spaces of Lie groups (57T15)
Related Items
Non-Kaehler heterotic string compactifications with non-zero fluxes and constant dilaton ⋮ On de Rham and Dolbeault cohomology of solvmanifolds ⋮ POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD -LEMMA ⋮ The cohomologies of the Iwasawa manifold and of its small deformations ⋮ Vertical-horizontal decomposition of Laplacians and cohomologies of manifolds with trivial tangent bundles ⋮ Dolbeault-Massey triple products of low degree ⋮ Rank of the Nijenhuis tensor on parallelizable almost complex manifolds ⋮ Construct holomorphic invariants in Čech cohomology by a combinatorial formula ⋮ Bott-Chern cohomology of solvmanifolds ⋮ Topological and geometric aspects of almost Kähler manifolds via harmonic theory ⋮ Techniques of computations of Dolbeault cohomology of solvmanifolds ⋮ Locally conformally Kähler solvmanifolds: a survey ⋮ Bott-Chern hypercohomology and bimeromorphic invariants ⋮ Hermitian geometry of Lie algebras with abelian ideals of codimension 2 ⋮ Ricci flatness of certain compact pseudo-Kähler solvmanifolds ⋮ Hard Lefschetz property for isometric flows ⋮ Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology ⋮ Holomorphic Poisson structure and its cohomology on nilmanifolds ⋮ The Kuranishi space of complex parallelisable nilmanifolds ⋮ Maximal nilpotent complex structures ⋮ Abelian \(J\)-invariant ideals on nilpotent Lie algebras ⋮ Complex product structures on 6-dimensional nilpotent Lie algebras ⋮ Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms ⋮ Invariant complex structures on tangent and cotangent Lie groups of dimension six ⋮ Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups ⋮ Holomorphic Poisson cohomology ⋮ Dolbeault cohomology for almost complex manifolds ⋮ Degree of non-Kählerianity for 6-dimensional nilmanifolds ⋮ Generalized deformation of complex structures on nilmanifolds ⋮ Deformations of Dolbeault cohomology classes for Lie algebra with complex structures ⋮ A family of complex nilmanifolds with in finitely many real homotopy types ⋮ Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds ⋮ Generalized deformations and holomorphic Poisson cohomology of solvmanifolds ⋮ Complex symplectic structures on Lie algebras ⋮ Dolbeault cohomology of compact nilmanifolds ⋮ On blow-ups and cohomology of almost complex manifolds ⋮ Dolbeault cohomologies of blowing up complex manifolds ⋮ Pseudo-Kähler metrics on six-dimensional nilpotent Lie algebras ⋮ Algebraic dimension of complex nilmanifolds ⋮ Dolbeault cohomologies of blowing up complex manifolds. II: Bundle-valued case ⋮ Complex, symplectic, and contact structures on low-dimensional Lie groups ⋮ Abelian complex structures and generalizations ⋮ STABILITY OF ABELIAN COMPLEX STRUCTURES ⋮ Dolbeault cohomology of nilmanifolds with left-invariant complex structure ⋮ The ascending central series of nilpotent Lie algebras with complex structure ⋮ \(p\)-Kähler and balanced structures on nilmanifolds with nilpotent complex structures ⋮ Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds ⋮ Complex nilmanifolds and Kähler-like connections ⋮ Complex structures on nilpotent Lie algebras with one-dimensional center ⋮ COMPLEX STRUCTURES ON STRATIFIED LIE ALGEBRAS ⋮ Locally conformal SKT structures ⋮ On the Bott–Chern cohomology and balanced Hermitian nilmanifolds ⋮ Invariant complex structures on 6-nilmanifolds: classification, Frölicher spectral sequence and special Hermitian metrics ⋮ On Strominger space forms ⋮ On a variational theorem of Gauduchon and torsion-critical manifolds
Cites Work
- Kähler and symplectic structures on nilmanifolds
- Complex parallelisable manifolds and their small deformations
- Real homotopy theory of Kähler manifolds
- On compact complex parallelisable solvmanifolds
- A general description of the terms in the Frölicher spectral sequence
- Applications of rational homotopy to geometry (results, problems, conjectures)
- Lectures on fibre bundles and differential geometry. Reissued
- The Frölicher spectral sequence for compact nilmanifolds
- On the cohomology of compact homogeneous spaces of nilpotent Lie groups
- Minimal Models of Nilmanifolds
- Complex Analytic Connections in Fibre Bundles
- On Automorphisms of A Kählerian Structure
- Dolbeault Homotopy Theory
- Shorter Notes: Some Simple Examples of Symplectic Manifolds
- On the Structure of Compact Complex Analytic Surfaces, I
- Complex Parallisable Manifolds
- RELATIONS BETWEEN THE COHOMOLOGY GROUPS OF DOLBEAULT AND TOPOLOGICAL INVARIANTS
- Symplectic manifolds with no Kähler structure
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item