Lectures on symplectic manifolds
Author(s)
Bibliographic Information
Lectures on symplectic manifolds
（Regional conference series in mathematics, no. 29）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1977
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
"Expository lectures from the CBMS regional conference held at the University of North Carolina, March 8-12, 1976."--T.p.verso
Bibliography: p. 45-48
Description and Table of Contents
Description
The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.
Table of Contents
Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations, intermediate polarizations Hamiltonian systems and group actions on symplectic manifolds Normal forms Lagrangian submanifolds and families of functions Intersection theory of lagrangian submanifolds Quantization on cotangent bundles Quantization and polarizations Quantizing lagrangian submanifolds and subspaces, construction of the Maslov bundle References.
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