Jholomorphic curves and symplectic topology
 Author/Creator
 McDuff, Dusa, 1945
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xiv, 726 p. ; 26 cm.
 Series
 Colloquium publications (American Mathematical Society) ; v. 52.
Access
Available online

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QA1 .A5225 V.52 2ND ED

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QA1 .A5225 V.52 2ND ED
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Contributors
 Contributor
 Salamon, D. (Dietmar)
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Symplectic and contact topology.
 Symplectic manifolds.
 Pseudoholomorphic curves.
 Differential geometry  Symplectic geometry, contact geometry  Symplectic manifolds, general.
 Differential geometry  Symplectic geometry, contact geometry  GromovWitten invariants, quantum cohomology, Frobenius manifolds.
 Differential geometry  Symplectic geometry, contact geometry  Global theory of symplectic and contact manifolds.
 Manifolds and cell complexes  Differential topology  Symplectic and contact topology.
 Dynamical systems and ergodic theory  Finitedimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems  General theory, relations with symplectic geometry and topology.
 Several complex variables and analytic spaces  Complex manifolds  Pseudoholomorphic curves.
 Differential geometry  Symplectic geometry, contact geometry  Lagrangian submanifolds; Maslov index.
 Differential geometry  Symplectic geometry, contact geometry  Floer homology and cohomology, symplectic aspects.
 Global analysis, analysis on manifolds  Partial differential equations on manifolds; differential operators  Elliptic equations on manifolds, general theory.
 Algebraic geometry  Projective and enumerative geometry  GromovWitten invariants, quantum cohomology, GopakumarVafa invariants, DonaldsonThomas invariants.
Bibliographic information
 Publication date
 2012
 Responsibility
 Dusa McDuff, Dietmar Salamon.
 Series
 American Mathematical Society colloquium publications ; v. 52
 ISBN
 9780821887462
 0821887467