Cohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group

DOI10.2307/2154798zbMath0836.57019OpenAlexW4249116506MaRDI QIDQ4321232

John F. Oprea, Gregory Lupton

Publication date: 6 May 1996

Full work available at URL: https://doi.org/10.2307/2154798

zbMATH Keywords

Sullivan minimal modelssymplectic actionscohomologically-symplectic manifoldssymplectic manifolds of Lefschetz typetoral actions on closed symplectic manifolds

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Rational homotopy theory (55P62) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Algebraic topology on manifolds and differential topology (57R19)

Related Items (23)

C-symplectic poset structure on a simply connected space ⋮ Topological complexity of symplectic manifolds ⋮ New bounds on the toral rank with applications to cohomologically symplectic spaces ⋮ A characterisation of symplectically aspherical manifolds ⋮ Embedded surfaces for symplectic circle actions ⋮ Non-Hamiltonian actions with isolated fixed points ⋮ Hard Lefschetz property for isometric flows ⋮ Pre-c-symplectic condition for the product of odd-spheres ⋮ Essential manifolds with extra structures ⋮ Discreteness of flux groups ⋮ The toral rank conjecture and variants of equivariant formality ⋮ Higher Lefschetz Traces and Spherical Euler Characteristics ⋮ \(L^2\)-cohomology and complete Hamiltonian manifolds ⋮ Formality and the Lefschetz property in symplectic and cosymplectic geometry ⋮ A C-symplectic free 𝑆¹-manifold with contractible orbits and 𝐂𝐀𝐓=\frac12𝐃𝐈𝐌 ⋮ Locally conformally symplectic and Kähler geometry ⋮ Category bounds for nonnegative Ricci curvature manifolds with infinite fundamental group ⋮ On fundamental groups of symplectically aspherical manifolds ⋮ A non-fixed point theorem for Hamiltonian lie group actions ⋮ Quotient maps, group actions and Lusternik-Schnirelmann category ⋮ Hereditary properties of co-Kähler manifolds ⋮ Self-closeness numbers of finite cell complexes ⋮ Symplectic theory of completely integrable Hamiltonian systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fixed points and torsion on Kähler manifolds
• Symplectic diffeomorphisms and the flux homomorphism
• The moment map for circle actions on symplectic manifolds
• G-actions and the fundamental group
• The moment map and equivariant cohomology
• Examples of simply-connected symplectic non-Kählerian manifolds
• New generalizations of Poincaré's geometric theorem
• Kähler and symplectic structures on nilmanifolds
• Exemples de variétés presque complexes. (Examples of almost complex manifolds)
• The topology of torus actions on symplectic manifolds. Transl. from the French by the author
• Obstruction to circle group actions preserving symplectic structure
• Symplectic structures on \(T^ 2\)-bundles over \(T^ 2\)
• The category of nilmanifolds
• Some remarks on symplectic actions of compact groups
• Nilpotent groups
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Symplectic manifolds and formality
• Splitting off tori and the evaluation subgroup of the fundamental group
• Injective operations of the toral groups
• Isometric imbedding of complex manifolds
• Factor spaces of solvable groups
• Kahler Structures on Compact Solvmanifolds
• MAXIMAL TORUS ACTIONS ON SOLVMANIFOLDS AND DOUBLE COSET SPACES
• The Trace of an Action and the Degree of a Map
• A Homotopical Conner-Raymond Theorem and a Question of Gottlieb
• Lie-Poisson Structure on Some Poisson Lie Groups
• Shorter Notes: Some Simple Examples of Symplectic Manifolds
• Fibrations with Compact Fibres
• Cuplength estimates on lagrangian intersections
• A Certain Subgroup of the Fundamental Group
• Evaluation Subgroups of Homotopy Groups
• Applications of Bundle Map Theory
• Symplectic manifolds with no Kähler structure

This page was built for publication: Cohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group