Introduction to Symplectic Topology

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Clarendon Press, 1998 - Mathematics - 486 pages
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Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behaviour of a wide range of physical systems. Over the last few years powerful new methods in analysis and topology have led to the development of the modern global theory ofsymplectic topology, including several striking and important results. At its publication in 1995, Introduction to Symplectic Topology was the first comprehensive introduction to the subject, and has since become an established text in this fast-developing area of mathematics. This second editionhas been significantly revised and expanded, with new references and examples added and theorems included or revised. A section has been included on new developments in the subject, and there is a more extensive discussion of Taubes and Donaldson's recent contributions to the subject.From reviews of the first edition: '...an authoritative and comprehensive reference...McDuff and Salamon have done an enormous service to the symplectic community: their book greatly enhances the accessibility of the subject to students and researchers alike.' Book Reviews, AMS
 

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Contents

Introduction
1
From classical to modern
11
Linear symplectic geometry
37
Symplectic manifolds
81
Almost complex structures
117
SYMPLECTIC MANIFOLDS
146
Symplectic Fibrations
197
Constructing Symplectic Manifolds
233
Generating functions
280
The group of symplectomorphisms
311
The Arnold conjecture
339
Symplectic capacities
371
New directions
417
References
458
Index
473
Copyright

Areapreserving diffeomorphisms
265

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About the author (1998)


Dusa McDuff is one of the world's leading researchers in this field, and has been invited to speak at the International Congress of Mathematicians 1998.

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