Symplectic Geometry, Groupoids, And Integrable Systems: Séminaire Sud Rhodanien De Géométrie à Berkeley (1989) (mathematical Sciences Research Institute Publications)

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 Groupoïdes de Lie et Groupoïdes Symplectiques....Pages 1-11 Géometrie Globale des Systèmes Hamiltoniens Complètement Intégrables et Variables Action-Angle avec Singularités....Pages 13-22 Sur Quelques Questions de Géométrie Symplectique....Pages 23-36 Intégration Symplectique des Variétés de Poisson Totalement Asphériques....Pages 37-72 La Première 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 R n et Variables Action-Angle avec Singularités....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