From Stein to Weinstein and back : symplectic geometry of affine complex manifolds /

Bibliographic Details
Main Author:	Cieliebak, Kai, 1966-
Other Authors:	Eliashberg, Y., 1946-
Format:	Book
Language:	English
Published:	Providence, R.I. : American Mathematical Society, [2012]
Series:	Colloquium publications (American Mathematical Society) ; v. 59.
Subjects:	Symplectic geometry. Stein manifolds. Several complex variables and analytic spaces > Complex manifolds > Stein manifolds. Differential geometry > Symplectic geometry, contact geometry > Global theory of symplectic and contact manifolds.

Table of Contents:

pt. 1. J-convexity. J-convex functions and hypersurfaces
Smoothing
Shapes for I-convex hypersurfaces
Some complex analysis
pt. 2. Existence of Stein structures. Symplectic and contact preliminaries
The h-principles
The existence theorem
pt. 3. Morse-Smale theory for J-convex functions. Recollections from Morse theory
Modifications of J-convex Morse functions
pt. 4. From Stein to Weinstein and back. Weinstein structures
Modifications of Weinstein structures
Existence revisited
Deformations of flexible Weinstein structures
Deformations of Stein structures
pt. 5. Stein manifolds and symplectic topology. Stein manifolds of complex dimension two
Exotic Stein structures
Appendix A: Some algebraic topology
Appendix B: Obstructions to formal Legendrian isotopies
Appendix C: Biographical notes on the main characters.