Book contents
- Frontmatter
- Contents
- Preface
- 1 The Arnold-Liouville theorem
- 2 Lagrangian fibrations
- 3 Global action-angle coordinates and torus actions
- 4 Symplectic reduction
- 5 Visible Lagrangian submanifolds
- 6 Focus-focus singularities
- 7 Examples of focus-focus systems
- 8 Almost toric manifolds
- 9 Surgery
- 10 Elliptic and cusp singularities
- Appendix A Symplectic linear algebra
- Appendix B Lie derivatives
- Appendix C Complex projective spaces
- Appendix D Cotangent bundles
- Appendix E Moser’s argument
- Appendix F Toric varieties revisited
- Appendix G Visible contact hypersurfaces and Reeb flows
- Appendix H Tropical Lagrangian submanifolds
- Appendix I Markov triples
- Appendix J Open problems
- References
- Index
4 - Symplectic reduction
Published online by Cambridge University Press: 06 July 2023
Book contents
- Frontmatter
- Contents
- Preface
- 1 The Arnold-Liouville theorem
- 2 Lagrangian fibrations
- 3 Global action-angle coordinates and torus actions
- 4 Symplectic reduction
- 5 Visible Lagrangian submanifolds
- 6 Focus-focus singularities
- 7 Examples of focus-focus systems
- 8 Almost toric manifolds
- 9 Surgery
- 10 Elliptic and cusp singularities
- Appendix A Symplectic linear algebra
- Appendix B Lie derivatives
- Appendix C Complex projective spaces
- Appendix D Cotangent bundles
- Appendix E Moser’s argument
- Appendix F Toric varieties revisited
- Appendix G Visible contact hypersurfaces and Reeb flows
- Appendix H Tropical Lagrangian submanifolds
- Appendix I Markov triples
- Appendix J Open problems
- References
- Index
Summary
We introduce symplectic reduction and symplectic cut, two constructions which yield a rich variety of new symplectic manifolds, including all the toric manifolds. We illustrate these constructions with many examples.
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- Lectures on Lagrangian Torus Fibrations , pp. 45 - 63Publisher: Cambridge University PressPrint publication year: 2023