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On the variation in the cohomology of the symplectic form of the reduced phase space

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References

  • [AM] Abraham, R., Marsden, J.E.: Foundations of mechanics. 2nd edition. Reading, Massachusetts, 1978

  • [A] Atiyah, M.F.: Convexity and commuting Hamiltonians, Bull. London Math. Soc.14, 1–15 (1982)

    Google Scholar 

  • [AS] Atiyah, M.F., Singer, I.M.: The index of elliptic operators III, Ann. of Math.87, 546–604 (1968)

    Google Scholar 

  • [GS1] Guillemin, V.W., Sternberg, S.: Convexity properties of the moment mapping. Invent. Math67, 491–513 (1982)

    Google Scholar 

  • [GS2] Guillemin, V.W., Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math.67, 515–538 (1982)

    Google Scholar 

  • [H] Harish-Chandra: Differential operators on a semisimple Lie algebra. Amer. J. Math.79, 87–120 (1957)

    Google Scholar 

  • [Hö] Hörmander, L.: Fourier integral operators I. Acta Math.127, 79–183 (1971)

    Google Scholar 

  • [K] Kirillov, A.A.: The characters of unitary representations of Lie groups. Funct. Anal. Appl.2, 133–146 (1968)

    Google Scholar 

  • [L] Lichnerowicz, A.: Théorie globale des connections et des groupes d'holonomie. Paris: Dunod 1955

    Google Scholar 

  • [S] Satake, l.: On a generalization of the notion of manifold. Proc. Natl. Acad. Sci. 359–363 (1956)

  • [Se] Serre, J-P.: Représentations linéaires et espaces homogènes Kählériennes des groupes de Lie compacts. Sém. Bourbaki 1953/54, Exposé 100

  • [W1] Weinstein, A.: Symplectic manifolds and their Lagrangian submanifolds. Adv. Math.6, 329–346 (1971)

    Google Scholar 

  • [W2] Weinstein, A.: On the volume of manifolds all of whosw geodesics are closed. J. Diff. Geom.9, 513–517 (1974)

    Google Scholar 

  • [W3] Weinstein, A.: SymplecticV-manifolds, periodic orbits of Hamiltonian systems and the volume of certain Riemannian manifolds. Comm. Pure Appl. Math.30, 265–271 (1977)

    Google Scholar 

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Partially supported by NSF Grant MC 80-23356 while visiting the University of California at Berkeley, U.S.A.

Supported in part by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.)

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Duistermaat, J.J., Heckman, G.J. On the variation in the cohomology of the symplectic form of the reduced phase space. Invent Math 69, 259–268 (1982). https://doi.org/10.1007/BF01399506

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