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Colloquium Publications: J-Holomorphic Curves and Symplectic Topology by Dusa McDuff and Dietmar Salamon (2012, Hardcover)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100821887467
ISBN-139780821887462
eBay Product ID (ePID)117228002
Product Key Features
Number of Pages726 Pages
Publication NameJ-Holomorphic Curves and Symplectic Topology
LanguageEnglish
SubjectGeometry / Differential, Topology, Geometry / Algebraic, Complex Analysis
Publication Year2012
FeaturesRevised
TypeTextbook
AuthorDusa Mcduff, Dietmar Salamon
Subject AreaMathematics
SeriesColloquium Publications
FormatHardcover
Dimensions
Item Height1.6 in
Item Weight50.9 Oz
Item Length10.4 in
Item Width7.4 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN2012-016161
Series Volume Number52
Edition DescriptionRevised edition
SynopsisThe main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology., 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 rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively 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.
LC Classification NumberQA613.59.M34 2012
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