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Book Review

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Book Information

Author(s): Izu Vaisman
Title: Lectures on the geometry of Poisson manifolds
Additional book information: Progress in Mathematics, vol. 118, Birkhäuser, Basel and Boston, 1994, vi + 205, $59.00, 3-7643-5016-4

References:

[Bo]
N. Bourbaki, Lie groups and Lie algebras, Part I, Springer-Verlag, Berlin and New York, 1989. MR 89k:17001

[Br]
J.-L. Brylinski, A differential complex for Poisson manifolds, J. Diff. Geom. 28 (1988), 93--114.MR 89m:58006

[C]
J. Conn, Normal forms for analytic Poisson structures, Ann. of Math. 119 (1984), 577--601; Normal forms for smooth Poisson structures, Ann. of Math. 121 (1985), 565--593.MR 86m:58050

[D]
P. M. Dirac, Lectures on quantum mechanics, Befer Graduate School Sci. Yeshiva Univ., New York, 1964.

[FS]
M. Flato and D. Sternheimer, Closedness of star products and cohomologies, Lie Theory and Geometry, in Honor of B. Kostant, Progress in Math. 123, Birkhäuser, New York, 1994. MR 1:327 536

[H]
R. Hermann, Cartan connections and the equivalence problem for geometric structures, Contributions to Differential Equations 3 (1964), 199--248. MR 29:2741

[Kir]
A. A. Kirillov, Local Lie algebras, Russian Math. Surveys 31 (1976), 57--76. MR 55:11304a

[Kar]
M. V. Karasev, Analogues of the objects of Lie group theory for nonlinear Poisson brackets, Math. USSR-Izv. 28 (1987), 497--527.

[KM]
M. V. Karasev and V. P. Maslov, Nonlinear Poisson brackets, geometry and quantization, Transl. Math. Monographs, vol. 119, Amer. Math. Soc., Providence, RI, 1993. MR 94a:58072

[Lie]
S. Lie, Theorie der transformationsgruppen (Zweiter Abschnitt, unter Mitwirkung von Prof. Dr. Friederich Engel), Teubner, Leipzig, 1890.

[Lic]
A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geom. 12 (1977), 253--300.MR 58:18565

[M]
K. C. H. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Mathematical Society Lecture Note Series, vol. 124, Cambridge University Press, 1987.

[MX]
K. C. H. Mackenzie and P. Xu, Lie bialgebroids and Poisson groupoids, Duke Math. J. 73 (1994), 415--452.MR 95B:58171

[W1]
A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), 523--557. MR 86i:58059

[W2]
------, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987), 101--104. MR 88c:58019

[W3]
------, Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan 40 (1988), 705--727. MR 90b:58091

[W4]
------, Deformation quantization, Sém. Bourbaki, 46ème année, no. 789 (1993-1994), Asterisque 227 (1995), 389--409. MR 1:321 655

Additional Information:

Reviewer(s):
Ping Xu
Affiliation: The Pennsylvania State University
Email: ping@math.psu.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 33 (1996), 255-261.
DOI: 10.1090/S0273-0979-96-00644-1
PII: S 0273-0979(96)00644-1
Copyright of article: Copyright 1996, American Mathematical Society

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