Overview

This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Ganduchan, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.

Full Product Details

Author:   Michele Audin ,  Jacques Lafontaine
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1994 ed.
Volume:   117
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.470kg
ISBN:  

9783764329976

ISBN 10:   3764329971
Pages:   331
Publication Date:   01 February 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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