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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. (English) Zbl 0503.58015

Invent. Math. 69, 259-268 (1982).
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Cited in 15 Reviews
Cited in 253 Documents

MathOverflow Questions:

Two questions on history of symplectic geometry in the 80’s

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
70H05 Hamilton’s equations

Keywords:

Hamiltonian torus action; Liouville measures; polynomial measure; momentum mapping; horizontal curves of a T-invariant connection; Chern class; canonical measure
PDFBibTeX XMLCite
\textit{J. J. Duistermaat} and \textit{G. J. Heckman}, Invent. Math. 69, 259--268 (1982; Zbl 0503.58015)
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References:

[1] [AM] Abraham, R., Marsden, J.E.: Foundations of mechanics. 2nd edition. Reading, Massachusetts, 1978
[2] [A] Atiyah, M.F.: Convexity and commuting Hamiltonians, Bull. London Math. Soc.14, 1-15 (1982) · Zbl 0482.58013 · doi:10.1112/blms/14.1.1
[3] [AS] Atiyah, M.F., Singer, I.M.: The index of elliptic operators III, Ann. of Math.87, 546-604 (1968) · Zbl 0164.24301 · doi:10.2307/1970717
[4] [GS1] Guillemin, V.W., Sternberg, S.: Convexity properties of the moment mapping. Invent. Math67, 491-513 (1982) · Zbl 0503.58017 · doi:10.1007/BF01398933
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[8] [K] Kirillov, A.A.: The characters of unitary representations of Lie groups. Funct. Anal. Appl.2, 133-146 (1968) · Zbl 0174.45001 · doi:10.1007/BF01075947
[9] [L] Lichnerowicz, A.: Théorie globale des connections et des groupes d’holonomie. Paris: Dunod 1955 · Zbl 0116.39101
[10] [S] Satake, l.: On a generalization of the notion of manifold. Proc. Natl. Acad. Sci. 359-363 (1956) · Zbl 0074.18103
[11] [Se] Serre, J-P.: Représentations linéaires et espaces homogènes Kählériennes des groupes de Lie compacts. Sém. Bourbaki 1953/54, Exposé 100
[12] [W1] Weinstein, A.: Symplectic manifolds and their Lagrangian submanifolds. Adv. Math.6, 329-346 (1971) · Zbl 0213.48203 · doi:10.1016/0001-8708(71)90020-X
[13] [W2] Weinstein, A.: On the volume of manifolds all of whosw geodesics are closed. J. Diff. Geom.9, 513-517 (1974) · Zbl 0289.53032
[14] [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) · Zbl 0339.58007 · doi:10.1002/cpa.3160300207
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