The cohomologies of the Iwasawa manifold and of its small deformations

DOI10.1007/s12220-011-9291-zzbMath1278.32013arXiv1212.4351OpenAlexW2070034275MaRDI QIDQ363217

Daniele Angella

Publication date: 2 September 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4351

zbMATH Keywords

de Rham cohomologyDolbeault cohomologyBott-Chern cohomologyAeppli cohomology

Mathematics Subject Classification ID

General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Homogeneous complex manifolds (32M10) Compact Kähler manifolds: generalizations, classification (32J27) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Deformations of complex structures (32G05)

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Cites Work

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• Complex analytic coordinates in almost complex manifolds
• On solvable generalized Calabi-Yau manifolds
• The jumping phenomenon of Hodge numbers
• Complex parallelisable manifolds and their small deformations
• Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with P. Cherenack
• Real homotopy theory of Kähler manifolds
• On compact complex parallelisable solvmanifolds
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• Techniques of computations of Dolbeault cohomology of solvmanifolds
• On deformations of complex analytic structures. III: Stability theorems for complex structures
• The Kuranishi space of complex parallelisable nilmanifolds
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• On the de Rham cohomology of solvmanifolds
• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Small Deformations of a Class of Compact Non-Kahler Manifolds
• Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
• Symplectic manifolds with no Kähler structure
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