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Lectures on Symplectic Manifolds

About this Title

Alan Weinstein, University of California, Berkeley, Berkeley, CA

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1977; Volume 29
ISBNs: 978-0-8218-1679-0 (print); 978-1-4704-2389-6 (online)
DOI: https://doi.org/10.1090/cbms/029
MathSciNet review: MR598470
MSC: Primary 58F05; Secondary 47G05, 53C15, 70Hxx

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Table of Contents

Front/Back Matter

Chapters

  • Introduction
  • Symplectic manifolds and lagrangian submanifolds, examples
  • Lagrangian splittings, real and complex polarizations, Kähler 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