Holomorphic Curves in Symplectic Geometry

348 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Progress in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Gruppen und Gruppentheorie
• ISBN: 9783034896566
• Sprache: Englisch
• Erscheinungsdatum: 28.10.2012
• Größe: 235 x 155 mm
• Verlag: Birkhäuser
• Herausgegeben von: Jacques Lafontaine, Michele Audin