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From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds
About this Title
Kai Cieliebak, Ludwig-Maximilians-Universität, München, Germany and Yakov Eliashberg, Stanford University, Stanford, CA
Publication: Colloquium Publications
Publication Year:
2012; Volume 59
ISBNs: 978-0-8218-8533-8 (print); 978-1-4704-1582-2 (online)
DOI: https://doi.org/10.1090/coll/059
MathSciNet review: MR3012475
MSC: Primary 53-02; Secondary 32E10, 32Q65, 53C15, 53D05, 58E05
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
Part 1. $J$-convexity
- Chapter 2. $J$-convex functions and hypersurfaces
- Chapter 3. Smoothing
- Chapter 4. Shapes for $i$-convex hypersurfaces
- Chapter 5. Some complex analysis
Part 2. Existence of Stein structures
- Chapter 6. Symplectic and contact preliminaries
- Chapter 7. The $h$-principles
- Chapter 8. The existence theorem
Part 3. Morse–Smale theory for $J$-convex functions
- Chapter 9. Recollections from Morse theory
- Chapter 10. Modifications of $J$-convex Morse functions
Part 4. From Stein to Weinstein and back
- Chapter 11. Weinstein structures
- Chapter 12. Modifications of Weinstein structures
- Chapter 13. Existence revisited
- Chapter 14. Deformations of flexible Weinstein structures
- Chapter 15. Deformations of Stein structures
Part 5. Stein manifolds and symplectic topology
- Chapter 16. Stein manifolds of complex dimension two
- Chapter 17. Exotic Stein structures
- Appendix A. Some algebraic topology
- Appendix B. Obstructions to formal Legendrian isotopies
- Appendix C. Biographical notes on the main characters