Modification and the cohomology groups of compact solvmanifolds

DOI10.1090/S1079-6762-07-00176-XzbMath1134.53024OpenAlexW1986062183MaRDI QIDQ5448857

Zhuang-Dan Guan

Publication date: 7 March 2008

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1079-6762-07-00176-x

zbMATH Keywords

cohomologyproductLie groupsymplectic manifoldsdecompositionssplittingshomogeneous spacecompact manifoldssolvmanifoldsfiber bundlesmodificationinvariant structureprealgebraic groupuniform discrete subgroupslocally flat parallelizable manifolds

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Differential geometry of homogeneous manifolds (53C30) Nilpotent and solvable Lie groups (22E25)

Related Items (8)

On de Rham and Dolbeault cohomology of solvmanifolds ⋮ Classification of compact complex homogeneous manifolds with pseudo-Kählerian structures ⋮ On classification of compact complex solvmanifolds ⋮ Formality and the Lefschetz property in symplectic and cosymplectic geometry ⋮ Solvable models for Kodaira surfaces ⋮ Invariant pseudo-Kähler metrics on generalized flag manifolds ⋮ Dolbeault cohomology of nilmanifolds with left-invariant complex structure ⋮ Symplectic harmonicity and generalized coeffective cohomologies

Cites Work

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• Plesiocompact homogeneous spaces
• The fundamental conjecture for homogeneous Kähler manifolds
• Classification of compact homogeneous pseudo-Kähler manifolds
• A splitting theorem for compact complex homogeneous spaces with a symplectic structure
• A pseudo-Kähler structure on a nontoral compact complex parallelizable colvmanifold
• Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms
• On compact symplectic manifolds with Lie group symmetries

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