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$J$-holomorphic Curves and Symplectic Topology: Second Edition

Dusa McDuff Barnard College, Columbia University, New York, NY
Dietmar Salamon ETH, Zurich, Switzerland
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Hardcover ISBN: 978-0-8218-8746-2
Product Code: COLL/52.R
List Price: $109.00 MAA Member Price:$98.10
AMS Member Price: $87.20 Electronic ISBN: 978-0-8218-9096-7 Product Code: COLL/52.R.E List Price:$109.00
MAA Member Price: $98.10 AMS Member Price:$87.20
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List Price: $163.50 MAA Member Price:$147.15
AMS Member Price: $130.80 Click above image for expanded view$J$-holomorphic Curves and Symplectic Topology: Second Edition Dusa McDuff Barnard College, Columbia University, New York, NY Dietmar Salamon ETH, Zurich, Switzerland Available Formats:  Hardcover ISBN: 978-0-8218-8746-2 Product Code: COLL/52.R  List Price:$109.00 MAA Member Price: $98.10 AMS Member Price:$87.20
 Electronic ISBN: 978-0-8218-9096-7 Product Code: COLL/52.R.E
 List Price: $109.00 MAA Member Price:$98.10 AMS Member Price: $87.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$163.50 MAA Member Price: $147.15 AMS Member Price:$130.80
• Book Details

Colloquium Publications
Volume: 522012; 726 pp
MSC: Primary 53; 57; 37; 32; Secondary 58; 14;

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its 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.

The main goal of this book is to establish 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 second edition clarifies various arguments, corrects several mistakes in the first edition, includes some additional results in Chapter 10 and Appendices C and D, and updates the references to recent developments.

Graduate students and research mathematicians interested in symplectic topology and geometry.

• Cover
• Title page
• Contents
• Preface to the second edition
• Preface
• Introduction
• 𝐽-holomorphic curves
• Moduli spaces and transversality
• Compactness
• Stable maps
• Moduli spaces of stable maps
• Gromov–Witten invariants
• Hamiltonian perturbations
• Applications in symplectic topology
• Gluing
• Quantum cohomology
• Floer homology
• Fredholm theory
• Elliptic regularity
• The Riemann–Roch theorem
• Stable curves of genus zero
• Singularities and intersections
• Bibliography
• List of symbols
• Index
• Back Cover

• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 522012; 726 pp
MSC: Primary 53; 57; 37; 32; Secondary 58; 14;

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its 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.

The main goal of this book is to establish 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 second edition clarifies various arguments, corrects several mistakes in the first edition, includes some additional results in Chapter 10 and Appendices C and D, and updates the references to recent developments.

Graduate students and research mathematicians interested in symplectic topology and geometry.

• Cover
• Title page
• Contents
• Preface to the second edition
• Preface
• Introduction
• 𝐽-holomorphic curves
• Moduli spaces and transversality
• Compactness
• Stable maps
• Moduli spaces of stable maps
• Gromov–Witten invariants
• Hamiltonian perturbations
• Applications in symplectic topology
• Gluing
• Quantum cohomology
• Floer homology
• Fredholm theory
• Elliptic regularity
• The Riemann–Roch theorem
• Stable curves of genus zero
• Singularities and intersections
• Bibliography
• List of symbols
• Index
• Back Cover
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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