Introduction to Symplectic Topology

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 of symplectic 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 edition has 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

1 - From classical to modern
2 - Linear symplectic geometry
3 - Symplectic manifolds
4 - Almost complex structures
5 - Symplectic group actions
6 - Symplectic fibrations
7 - Constructing symplectic manifolds
8 - Area-preserving diffeomorphisms
9 - Generating functions
10 - The group of symplectomorphisms
11 - The Arnold conjecture
12 - Symplectic capacities
13 - New directions

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.