J-Holomorphic Curves and Symplectic Topology

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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 als...
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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 Gromovs 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.
Uitgever Turpin distribution services ltd
Druk 0
ISBN/EAN 9780821887462
Auteur McDuff, Dusa
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