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.
Inhaltsverzeichnis
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.
