From Stein to Weinstein and back : symplectic geometry of affine complex manifolds / Kai Cieliebak, Yakov Eliashberg.

• 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.

Ämnesord

Symplectic geometry.  (LCSH)

Stein manifolds.  (LCSH)

Several complex variables and analytic spaces -- Complex manifolds -- Stein manifolds.  (msc)

Differential geometry -- Symplectic geometry, contact geometry -- Global theory of symplectic and contact manifolds.  (msc)

Differentialgeometri  (sao)

Klassifikation

515.946 (DDC)

32Q28 (msc)

53D35 (msc)

Tdh (kssb/8 (machine generated))