Holomorphic Curves in Symplectic Geometry

Mitwirkende
Herausgegeben von	Michele Audin
Herausgegeben von	Jacques Lafontaine

Introduction: Applications of pseudo-holomorphic curves to symplectic topology.
1 Examples of problems and results in symplectic topology.
2 Pseudo-holomorphic curves in almost complex manifolds.
3 Proofs of the symplectic rigidity results.
4 What is in the book… and what is not.
1: Basic symplectic geometry.
I An introduction to symplectic geometry.
II Symplectic and almost complex manifolds.
2: Riemannian geometry and linear connections.
III Some relevant Riemannian geometry.
IV Connexions linéaires, classes de Chern, théorème de Riemann-Roch.
3: Pseudo-holomorphic curves and applications.
V Some properties of holomorphic curves in almost complex manifolds.
VI Singularities and positivity of intersections of J-holomorphic curves.
VII Gromov’s Schwarz lemma as an estimate of the gradient for holomorphic curves.
VIII Compactness.
IX Exemples de courbes pseudo-holomorphes en géométrie riemannienne.
X Symplectic rigidity: Lagrangian submanifolds.
Authors’ addresses.