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Coisotropic calculus and Poisson groupoids
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1988 Volume 40 Issue 4 Pages 705-727
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- Published: 1988 Received: October 13, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [A-M] R. Almeida and P. Molino, Suites d'Atiyah et feuilletages transversalement complets, C.R. Acad. Sci. Paris, 300 (1985), 13-15.
[Av] G. Alvarez-Sanchez, Geometric methods of classical mechanics applied to control theory, Ph. D. Thesis, University of California, Berkeley, 1986.
[B] R. Brown, Higher-dimensional Group Theory, Low-Dimensional Topology (Brown and Thickstun eds.), I, Cambridge University Press, 1982, pp. 215-238.
[C1] J. F. Conn, Normal forms for analytic Poisson structures, Ann. of Math., 119 (1984), 577-601.
[C2] J. F. Conn, Normal forms for smooth Poisson structures, Ann. of Math., 121 (1985), 565-593.
[Cs] A. Connes, Sur la théorie non commutative de l'intégration, Algèbres d'Opérateurs, Lecture Notes in Math., 725, Springer, 1979, pp. 19-143.
[Ct-D-W] A. Coste, P. Dazord et A. Weinstein, Groupoïdes symplectiques, Publications du Département de Mathématiques, Université Claude Bernard-Lyon I, 2/A, 1987.
[Cu] T. J. Courant, Dirac manifolds, Ph. D. Thesis, University of California, Berkeley, 1987.
[D] V. G. Drinfel'd, Hamiltonian structures on Lie groups, Lie bialgebras, and the geometric meaning of the classical Yang-Baxter equations, Soviet Math. Dokl., 27 (1983), 68-71.
[E] C. Ehresmann, Structures feuilletées, Proc. 5th Canadian Math. Congress, Montreal, 1961, pp. 109-172.
[G] M. Gotay, On coisotropic embeddings of presymplectic manifolds, Proc. Amer. Math. Soc., 84 (1982), 111-114.
[Gu] V. Guillemin, Clean intersections and Fourier integrals, Fourier Integral Operators and Partial Differential Equations, Lecture Notes in Math., 459, Springer, 1975, pp. 23-35.
[Gu-S1] V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, 14, Amer. Math. Soc., Providence, 1977.
[Gu-S2] V. Guillemin and S. Sternberg, Some problems in integral geometry and some related problems in microlocal analysis, Amer. J. Math., 101 (1979), 915-955.
[K] M. V. Karasev, Analogues of objects of Lie group theory for nonlinear Poisson brackets, Math. USSR-Izv., 28 (1987), 497-527.
[Ko] J.-L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Élie Cartan et les mathématiques d'aujourdhui, Astérisque (hors série), (1985), 257-271.
[L] P. Libermann, Problemes d'équivalence et géométrie symplectique, IIIe rencontre de géométrie du Schnepfenried,10-15 mai 1982, I., Astérisque, 107-108 (1983), 43-68.
[M] K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, LMS, Lecture Notes Series, 124, Cambridge Univ. Press, 1987.
[Ma-R] J. E. Marsden and T. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys., 11 (1986), 161-169.
[Mi-W] K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoids, Publ. RIMS, Kyoto Univ., 24 (1988), 121-140.
[Ml] P. Molino, Structure transverse aux orbites de la representation coadjointe: le cas des orbites réductives, Sem. Geom. Diff., (Université des Sciences et Techniques du Languedoc, Montpellier, 1983-84), 55-62.
[Mn] R. Montgomery, The bundle picture in mechanics, Ph. D. Thesis, University of California, Berkeley, 1986.
[S] M. A. Semenov-Tian-Shansky, Dressing transformations and Poisson group actions, Publ. RIMS, Kyoto University, 21 (1985), 1237-1260.
[St] S. Sternberg, Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field, Proc. Nat. Acad. Sci. U.S.A., 74 (1977), 5253-5254.
[W1] A. Weinstein, Symplectic manifolds and their lagrangian submanifolds, Adv. in Math., 6 (1971), 329-346.
[W2] A. Weinstein, A universal phase space for particles in Yang-Mills fields, Lett. Math. Phys., 2 (1978), 417-420.
[W3] A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc., 5 (1981), 1-13.
[W4] A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom., 18 (1983), 523-557.
[W5] A. Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc., 16 (1987), 101-104.
[Wi] H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom., 1 (1983), 51-75.
Right : [A-M] R. Almeida and P. Molino, Suites d'Atiyah et feuilletages transversalement complets, C.R. Acad. Sci. Paris, 300 (1985), 13-15.
[Av] G. Alvarez-Sanchez, Geometric methods of classical mechanics applied to control theory, Ph. D. Thesis, University of California, Berkeley, 1986.
[B] R. Brown, Higher-dimensional Group Theory, Low-Dimensional Topology (Brown and Thickstun eds.), I, Cambridge University Press, 1982, pp. 215-238.
[C1] J. F. Conn, Normal forms for analytic Poisson structures, Ann. of Math., 119 (1984), 577-601.
[C2] J. F. Conn, Normal forms for smooth Poisson structures, Ann. of Math., 121 (1985), 565-593.
[Cs] A. Connes, Sur la théorie non commutative de l'intégration, Algèbres d'Opérateurs, Lecture Notes in Math., 725, Springer, 1979, pp. 19-143.
[Ct-D-W] A. Coste, P. Dazord et A. Weinstein, Groupoïdes symplectiques, Publications du Département de Mathématiques, Université Claude Bernard-Lyon I, 2/A, 1987.
[Cu] T. J. Courant, Dirac manifolds, Ph. D. Thesis, University of California, Berkeley, 1987.
[D] V. G. Drinfel'd, Hamiltonian structures on Lie groups, Lie bialgebras, and the geometric meaning of the classical Yang-Baxter equations, Soviet Math. Dokl., 27 (1983), 68-71.
[E] C. Ehresmann, Structures feuilletées, Proc. 5th Canadian Math. Congress, Montreal, 1961, pp. 109-172.
[G] M. Gotay, On coisotropic embeddings of presymplectic manifolds, Proc. Amer. Math. Soc., 84 (1982), 111-114.
[Gu] V. Guillemin, Clean intersections and Fourier integrals, Fourier Integral Operators and Partial Differential Equations, Lecture Notes in Math., 459, Springer, 1975, pp. 23-35.
[Gu-S1] V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, 14, Amer. Math. Soc., Providence, 1977.
[Gu-S2] V. Guillemin and S. Sternberg, Some problems in integral geometry and some related problems in microlocal analysis, Amer. J. Math., 101 (1979), 915-955.
[K] M. V. Karasev, Analogues of objects of Lie group theory for nonlinear Poisson brackets, Math. USSR-Izv., 28 (1987), 497-527.
[Ko] J. -L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Élie Cartan et les mathématiques d'aujourdhui, Astérisque (hors série), (1985), 257-271.
[L] P. Libermann, Problemes d'équivalence et géométrie symplectique, IIIe rencontre de géométrie du Schnepfenried,10-15 mai 1982, I., Astérisque, 107-108 (1983), 43-68.
[M] K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry, LMS, Lecture Notes Series, 124, Cambridge Univ. Press, 1987.
[Ma-R] J. E. Marsden and T. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys., 11 (1986), 161-169.
[Mi-W] K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoids, Publ. RIMS, Kyoto Univ., 24 (1988), 121-140.
[Ml] P. Molino, Structure transverse aux orbites de la representation coadjointe: le cas des orbites réductives, Sem. Geom. Diff., (Université des Sciences et Techniques du Languedoc, Montpellier, 1983-84), 55-62.
[Mn] R. Montgomery, The bundle picture in mechanics, Ph. D. Thesis, University of California, Berkeley, 1986.
[S] M. A. Semenov-Tian-Shansky, Dressing transformations and Poisson group actions, Publ. RIMS, Kyoto University, 21 (1985), 1237-1260.
[St] S. Sternberg, Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field, Proc. Nat. Acad. Sci. U. S. A., 74 (1977), 5253-5254.
[W1] A. Weinstein, Symplectic manifolds and their lagrangian submanifolds, Adv. in Math., 6 (1971), 329-346.
[W2] A. Weinstein, A universal phase space for particles in Yang-Mills fields, Lett. Math. Phys., 2 (1978), 417-420.
[W3] A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc., 5 (1981), 1-13.
[W4] A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom., 18 (1983), 523-557.
[W5] A. Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc., 16 (1987), 101-104.
[Wi] H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom., 1 (1983), 51-75.
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