9780821834855
J-Holomorphic Curves And Symplectic Topology (Colloquium Publications (Amer Mathematical Soc)) - Dusa McDuff, Dietmar Salamon
American Mathematical Society (2004)
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#3907

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Pseudoholomorphic curves, Symplectic and contact topology, Symplectic manifolds

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.

Product Details
LoC Classification QA613.59 .M34 2004
Dewey 516.36
Format Hardcover
Cover Price 104,00 €
No. of Pages 669
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