Holomorphic curves in symplectic geometry
type: Item
instance of: scholarly article
title: Holomorphic curves in symplectic geometry
zbMATH Open document ID: 0802.53001
published in: Progress in Mathematics
publication date: 1994-05-17T00:00:00Z
review text: The articles of this volume will not be indexed individually. The book is based on lectures given in a CIMPA summer school, held in Sophia-Antipolis, France in July 1992. The aim of the school was to understand in some detail the techniques and results of the famous paper by \textit{M. Gromov} [Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)]. A short introductory chapter written by the editors contains a very clear description of some problems in symplectic topology and Gromov's way to solve them. Chapters I--IV are devoted to some basic facts in symplectic geometry, almost complex manifolds, Riemannian geometry, Chern characteristic classes. Then the technical part of the book is started. Chapters V, VI are devoted to analytic and geometric aspects of the theory of pseudo-holomorphic curves, chapter VII gives a proof of Gromov version of the classical Schwarz lemma, which is a main tool in the proof of the Gromov compactness theorem given in chapter VIII. In chapter IX, pseudo-holomorphic curves are shown to appear also in Riemannian geometry. The developed technique is actively exploited in the last chapter X, which gives a panoramic view of Lagrangian submanifolds and related subjects. The book contains contributions of the following specialists, besides the editors: A. Banyaga, P. Gauduchon, F. Labourie, F. Lalonde, Gang liu, D. Mcduff and M.-P. Muller, P. Pansu, L. Polterovich, J. C. Sikorav. The exposition is essentially self-contained, and, in my opinion, the book should be useful to any mathematician, who is interested in symplectic topology, including graduated students.
Mathematics Subject Classification ID: 53-06
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 568731
zbMATH Keywords: Holomorphic curves
zbMATH Keywords: Symplectic geometry
zbMATH Keywords: symplectic topology
zbMATH Keywords: almost complex manifolds
zbMATH Keywords: Chern characteristic classes
zbMATH Keywords: pseudo-holomorphic curves
zbMATH Keywords: Schwarz lemma
zbMATH Keywords: Gromov compactness theorem
zbMATH Keywords: Lagrangian submanifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 568731