Ebook: Symplectic Geometry, Groupoids, and Integrable Systems: Séminaire Sud Rhodanien de Géométrie à Berkeley (1989)

The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.

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The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.
Content:
Front Matter....Pages i-xi
Groupo?des de Lie et Groupo?des Symplectiques....Pages 1-11
G?ometrie Globale des Syst?mes Hamiltoniens Compl?tement Int?grables et Variables Action-Angle avec Singularit?s....Pages 13-22
Sur Quelques Questions de G?om?trie Symplectique....Pages 23-36
Int?gration Symplectique des Vari?t?s de Poisson Totalement Asph?riques....Pages 37-72
La Premi?re Classe de Chern Comme Obstruction `la Quantification Asymptotique....Pages 73-97
Groupes de Poisson Affines....Pages 99-128
Singular Lagrangian Foliation Associated to an Integrable Hamiltonian Vector Field....Pages 129-136
Hyperbolic Actions of R p on Poisson Manifolds....Pages 137-150
Compactification d’Actions de ? n et Variables Action-Angle avec Singularit?s....Pages 151-167
On the Diameter of the Symplectomorphism Group of the Ball....Pages 169-172
A Symplectic Analogue of the Mostow-Palais Theorem....Pages 173-182
Melnikov Formulas For Nearly Integrable Hamiltonian Systems....Pages 183-188
A Non-Linear Hadamard Theorem....Pages 189-192
Equivariant Prequantization....Pages 193-207
Momentum Mappings And Reduction of Poisson Actions....Pages 209-226
On Jacobi Manifolds and Jacobi Bundles....Pages 227-246
Groupes de Lie `Structure Symplectique Invariante....Pages 247-266
Holonomy Groupoids of Generalized Foliations. II. Transverse Measures and Modular Classes....Pages 267-279
Symplectic Groupoids, Geometric Quantization, and Irrational Rotation Algebras....Pages 281-290
Morita Equivalent Symplectic Groupoids....Pages 291-311

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The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.
Content:
Front Matter....Pages i-xi
Groupo?des de Lie et Groupo?des Symplectiques....Pages 1-11
G?ometrie Globale des Syst?mes Hamiltoniens Compl?tement Int?grables et Variables Action-Angle avec Singularit?s....Pages 13-22
Sur Quelques Questions de G?om?trie Symplectique....Pages 23-36
Int?gration Symplectique des Vari?t?s de Poisson Totalement Asph?riques....Pages 37-72
La Premi?re Classe de Chern Comme Obstruction `la Quantification Asymptotique....Pages 73-97
Groupes de Poisson Affines....Pages 99-128
Singular Lagrangian Foliation Associated to an Integrable Hamiltonian Vector Field....Pages 129-136
Hyperbolic Actions of R p on Poisson Manifolds....Pages 137-150
Compactification d’Actions de ? n et Variables Action-Angle avec Singularit?s....Pages 151-167
On the Diameter of the Symplectomorphism Group of the Ball....Pages 169-172
A Symplectic Analogue of the Mostow-Palais Theorem....Pages 173-182
Melnikov Formulas For Nearly Integrable Hamiltonian Systems....Pages 183-188
A Non-Linear Hadamard Theorem....Pages 189-192
Equivariant Prequantization....Pages 193-207
Momentum Mappings And Reduction of Poisson Actions....Pages 209-226
On Jacobi Manifolds and Jacobi Bundles....Pages 227-246
Groupes de Lie `Structure Symplectique Invariante....Pages 247-266
Holonomy Groupoids of Generalized Foliations. II. Transverse Measures and Modular Classes....Pages 267-279
Symplectic Groupoids, Geometric Quantization, and Irrational Rotation Algebras....Pages 281-290
Morita Equivalent Symplectic Groupoids....Pages 291-311
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