References
Arnol'd, V.I., Givental, A.B.: Symplectic geometry. In: Arnol'd, V.I., Novikov, S.P. (eds.) Dynamical systems 4. (Encycl. Math. Sci., vol. 4, pp. 1–136). Berlin Heidelberg New York: Springer 1990
Atiyah, M., Bott, R.: The moment map and equivariant cohomology. Topology23, 1–28 (1984)
Bott, R.: Lectures on Morse theory, Old and new. Bull. Am. Math. Soc., New Ser.7, 331–358 (1982)
Borel, A., et al.: Seminar on Transformation Groups. (Ann. Math. Stud., vol. 46) Princeton, NJ: Princeton University Press 1961
Bourbaki, N.: Eléments de Mathématique. Groupes at Algébres de Lie, Chap. 9: Groupes de Lie Réels Compacts. Paris: Masson 1982
Cartan, H., Eilenberg, S.: Homological Algebra. Princeton, NJ: Princeton University Press 1956
Duistermaat, J.J., Heckman, G.J.: On the variation in the cohomology of the symplectic form of the reduced phase space; Addendum. Invent. Math.69, 259–269 (1982);72, 153–158 (1983)
Frankel, T.: Homology and flows on manifolds. Ann. Math.65, 331–339 (1957)
Frankel, T.: Fixed points on Kähler manifolds. Ann. Math.70, 1–8 (1959)
Ginzburg, V.L.: On closed characteristics of 2-forms. Thesis, Berkeley (1990)
Givental, A.B.: Periodic maps in symplectic topology. Funct. Anal. Appl.23 (no. 4), 37–52 (1989)
Hsiang, W.Y.: Cohomology theory of topological transformation groups. Berlin Heidelberg New York: Springer 1975
Kirwan, F.: Cohomology of quotients in symplectic and algebraic geometry. (Math. Notes, Princeton, vol. 31) Princeton: Princeton University Press 1984
Kostant, B.: Quantization and Unitary Representations. (Lect. Notes Math., vol. 170, pp. 87–208) Berlin Heidelberg New York: Springer 1970
McDuff, D.: The moment map for circle actions on symplectic manifolds. J. Geom. Phys.5, 149–161 (1988)
Ono, K.: Equivariant projective imbeddings theorem for symplectic manifolds. J. Fac. Sci. Univ. Tokyo, Sect. IA Math.35, 381–392 (1988)
Ono, K.: Obstruction to circle action preserving symplectic structure (Preprint)
Turiel, F.J.: Dimension minimale des orbites d'une action symplectique deR n sur une variété compacte. In: Sem. Gaston Daboux de geomémtrie et topologie différentielle, 1987–1988. Univ. de Sci. et Tech. du Languedoc, Inst. de Math. 1988
Weinstein, A.: SymplecticV-manifold, periodic orbits of Hamiltonian systems and the volume of certain Riemannian manifolds. Commun. Pure Appl. Math.30, 265–271 (1977)
Author information
Authors and Affiliations
Additional information
The Research was partially supported by NSF Grant DMS 8505550
Rights and permissions
About this article
Cite this article
Ginzburg, V.L. Some remarks on symplectic actions of compact groups. Math Z 210, 625–640 (1992). https://doi.org/10.1007/BF02571819
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571819