Overview

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. Its mathematical applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical physics, it provides a natural context in which to define Gromov-Witten invariants and quantum cohomology-two important ingredients of the mirror symmetry conjecture. This book establishes the fundamental theorems of the subject in full and rigorous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associativity of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology: There are two long chapters on applications, one concentrating on classical results in symplectic topology and the other concerned with quantum cohomology. The last chapter sketches some recent developments in Floer theory. The five appendices of the book provide necessary background related to the classical theory of linear elliptic operators, Fredholm theory, Sobolev spaces, as well as a discussion of the moduli space of genus zero stable curves and a proof of the positivity of intersections of $J$-holomorphic curves in four dimensional manifolds. The book is suitable for graduate students and researchers interested in symplectic geometry and its applications, especially in the theory of Gromov-Witten invariants.

Full Product Details

Author:   Dusa McDuff ,  Dietmar Salamon
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   illustrated edition
Volume:   No. 52
Dimensions:   Width: 18.70cm , Height: 3.90cm , Length: 26.10cm
ISBN:  

9780821834855

ISBN 10:   0821834851
Pages:   669
Publication Date:   01 May 2004
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you.

Table of Contents

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions