Some remarks on symplectic actions of compact groups

DOI10.1007/BF02571819zbMath0759.57023MaRDI QIDQ1202212

Viktor L. Ginzburg

Publication date: 2 February 1993

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174424

zbMATH Keywords

fixed pointsequivariant cohomologysymplectic manifoldcohomologically free actionsymplectic action of a torussymplectic actions of compact groupssymplectic non-Hamiltonian circle action

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)

Related Items (12)

The stratified spaces of a symplectic Lie group action ⋮ Non-Hamiltonian actions with isolated fixed points ⋮ Topology of symplectic torus actions with symplectic orbits ⋮ The reduced spaces of a symplectic Lie group action ⋮ Hamiltonian and symplectic symmetries: An introduction ⋮ \(L^2\)-cohomology and complete Hamiltonian manifolds ⋮ EQUIVARIANT POISSON COHOMOLOGY AND A SPECTRAL SEQUENCE ASSOCIATED WITH A MOMENT MAP ⋮ Diffeomorphism groups of compact manifolds ⋮ Symplectic torus actions with coisotropic principal orbits ⋮ Symmetry reduction in symplectic and Poisson geometry ⋮ Cohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group ⋮ Symplectic theory of completely integrable Hamiltonian systems

Cites Work

• Periodic maps in symplectic topology
• Homology and flows on manifolds
• Fixed points and torsion on Kähler manifolds
• The moment map for circle actions on symplectic manifolds
• The moment map and equivariant cohomology
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Obstruction to circle group actions preserving symplectic structure
• Sheaves on a loop group and Langlands duality
• Symplectic v‐manifolds, periodic orbits of hamiltonian systems, and the volume of certain riemannian manifolds
• Lectures on Morse theory, old and new
• Quantization and unitary representations
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