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 McDuff, Dusa, 1945
 Providence, R.I. : American Mathematical Society, c2004.
 Description
 Book — xii, 669 p. : ill. ; 27 cm.
 Summary

 Introduction $J$holomorphic curves Moduli spaces and transversality Compactness Stable maps Moduli spaces of stable maps GromovWitten invariants Hamiltonian perturbations Applications in symplectic topology Gluing Quantum cohomology Floer cohomology Fredholm theory Elliptic regularity The RiemannRoch theorem Stable curves of genus zero Singularities and intersections (written with Laurent Lazzarini) Bibliography List of symbols Index.
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QA1 .A5225 V.52  Unknown 
 Wendl, Chris, author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2020
 Description
 Book — viii, 185 pages : illustrations ; 24 cm
 Summary

 Introduction
 1. Closed holomorphic curves in symplectic 4manifolds
 2. Intersections, ruled surfaces and contact boundaries
 3. Asymptotics of punctured holomorphic curves
 4. Intersection theory for punctured holomorphic curves
 5. Symplectic fillings of planar contact 3manifolds Appendix A. Properties of pseudoholomorphic curves Appendix B. Local positivity of intersections Appendix C. A quick survey of Siefring's intersection theory References Index.
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 McDuff, Dusa, 1945
 2nd ed.  Providence, R.I. : American Mathematical Society, c2012.
 Description
 Book — xiv, 726 p. ; 26 cm.
 Summary

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 GromovWitten 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 fourdimensional 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.
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QA1 .A5225 V.52 2ND ED  Unknown 
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