Bulletin of the American Mathematical Society

MathSciNet review: 1567989
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Book Information:

Author: Mich\`ele Audin
Title: The topology of torus actions on symplectic manifolds
Additional book information: Birk\-h\"auser-Verlag, Basel, Boston, and Berlin, 1991, 181 pp., US$64.00. ISBN3-7643-2602-6, ISBN 0-8176-2602-6.

M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15. MR 642416, DOI 10.1112/blms/14.1.1

M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28. MR 721448, DOI 10.1016/0040-9383(84)90021-1

Michèle Audin, Hamiltoniens périodiques sur les variétés symplectiques compactes de dimension $4$, Géométrie symplectique et mécanique (La Grande Motte, 1988) Lecture Notes in Math., vol. 1416, Springer, Berlin, 1990, pp. 1–25 (French). MR 1047474, DOI 10.1007/BFb0097462

Nicole Berline and Michèle Vergne, Zéros d’un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J. 50 (1983), no. 2, 539–549 (French). MR 705039

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Thomas Delzant, Hamiltoniens périodiques et images convexes de l’application moment, Bull. Soc. Math. France 116 (1988), no. 3, 315–339 (French, with English summary). MR 984900

J. J. Duistermaat and G. J. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), no. 2, 259–268. MR 674406, DOI 10.1007/BF01399506

Viktor L. Ginzburg, Some remarks on symplectic actions of compact groups, Math. Z. 210 (1992), no. 4, 625–640. MR 1175727, DOI 10.1007/BF02571819

V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), no. 3, 491–513. MR 664117, DOI 10.1007/BF01398933

V. Guillemin and S. Sternberg, Birational equivalence in the symplectic category, Invent. Math. 97 (1989), no. 3, 485–522. MR 1005004, DOI 10.1007/BF01388888

Frances Clare Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol. 31, Princeton University Press, Princeton, NJ, 1984. MR 766741, DOI 10.2307/j.ctv10vm2m8

V. Guillemin and S. Sternberg, Convexity properties of the moment mapping. II, Invent. Math. 77 (1984), no. 3, 533–546. MR 759258, DOI 10.1007/BF01388837

Dusa McDuff, The moment map for circle actions on symplectic manifolds, J. Geom. Phys. 5 (1988), no. 2, 149–160. MR 1029424, DOI 10.1016/0393-0440(88)90001-0

[S]

I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf der Determinanten-theory, Sitzungsber. Berlin. Math. Ges. 22 (1923), 9-20.

[At]

M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. MR 642416 (83e:53037)

[AB]

M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28. MR 721448 (85e:58041)

[Au]

M. Audin, Hamiltoniens périodique sur les variétés symplectique compactes de dimension 4, Géométrie symplectique et mécanique, Proceedings 1988 (C. Albert, ed.), Lecture Notes in Math., vol. 1416, Springer-Verlag, Berlin and New York, 1990. MR 1047474 (91f:57013)

[BV]

N. Berline and M. Vergne, Zéros d'un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J. 50 (1983), 539-549. MR 705039 (84i:58114)

[B]

A. Borel et al., Seminar on transformation groups, Ann. of Math. Stud., vol. 46, Princeton Univ. Press, Princeton, NJ, 1961. MR 0116341 (22:7129)

[D]

T. Delzant, Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988), 315-339. MR 984900 (90b:58069)

[DH]

J. J. Duistermaat and G. J. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space; Addendum, Invent. Math. 69 (1982), 259-269, 72 (1983), 153-158. MR 674406 (84h:58051a)

[G]

V. L. Ginzburg, Some remarks on symplectic actions of compact groups, Math. Z. (to appear, 1992). MR 1175727 (93h:57053)

[GS1]

V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513. MR 664117 (83m:58037)

[GS2]

-, Birational equivalence in symplectic geometry, Invent. Math. 97 (1989), 485-551. MR 1005004 (90f:58060)

[K1]

F. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Math. Notes, vol. 31, Princeton Univ. Press, Princeton, NJ, 1984. MR 766741 (86i:58050)

[K2]

-, Convexity properties of the moment mapping, III, Invent. Math 77 (1984), 547-552. MR 759257 (86b:58042b)

[M]

D. McDuff, The moment map for circle actions on symplectic manifolds, J. Geom. Phys. 5 (1988), 149-161. MR 1029424 (91c:58042)

[S]

I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf der Determinanten-theory, Sitzungsber. Berlin. Math. Ges. 22 (1923), 9-20.