Introduction to Symplectic Topology

Third Edition

Dusa McDuff and Dietmar Salamon

Oxford Graduate Texts in Mathematics

Can be used as an introductory textbook for graduate students or mature mathematicians who are interested in symplectic topology but are as yet unfamiliar with the subject.
All chapters have been revised to improve the exposition and to make them more readable, new material has been added in many places, and various proofs have been tightened up.
Copious new references to key papers have been added to the bibliography.
Chapter 13 has been completely rewritten and has a new title (Questions of Existence and Uniqueness).
A new Chapter 14 on open problems in the field has been added.

New to this Edition:

All chapters have been revised to improve the exposition and to make them more readable, new material has been added in many places, and various proofs have been tightened up. Copious new references to key papers have been added to the bibliography.
A section on GIT has been added to Chapter 5.
The material on contact geometry in Chapter 3 has been expanded.
Chapter 13 has been completely rewritten and has a new title (Questions of Existence and Uniqueness). It now contains an introduction to existence and uniqueness problems in symplectic topology, a section an various examples, an overview of Taubes-Seiberg-Witten theory and its applications to symplectic topology, and a section on symplectic 4-manifolds.
A new Chapter 14 on open problems in the field has been added.

Introduction to Symplectic Topology

Third Edition

Dusa McDuff and Dietmar Salamon

Oxford Graduate Texts in Mathematics

Description

Over the last number of 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. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

Introduction to Symplectic Topology

Third Edition

Dusa McDuff and Dietmar Salamon

Oxford Graduate Texts in Mathematics

FOUNDATIONS
1. From classical to modern
2. Linear symplectic geometry
3. Symplectic manifolds
4. Almost complex structures
SYMPLECTIC MANIFOLDS
5. Symplectic group actions
6. Symplectic Fibrations
7. Constructing Symplectic Manifolds
SYMPLECTOMORPHISMS
8. Area-preserving dieomorphisms
9. Generating functions
10. The group of symplectomorphisms
SYMPLECTIC INVARIANTS
11. The Arnold conjecture
12. Symplectic capacities
13. Questions of existence and uniqueness
14. Open problems
A. Smooth Maps

Introduction to Symplectic Topology

Third Edition

Dusa McDuff and Dietmar Salamon

Oxford Graduate Texts in Mathematics

Author Information

Dusa McDuff, Professor of Mathematics, Columbia University,Dietmar Salamon, Professor of Mathematics, ETH Zurich

Dusa McDuff was born in London, UK, in 1945. She studied Mathematics at the University of Edinburgh (B. Sc. (Hon) in 1967), at Cambridge University (Ph. D. in 1971, supervised by G.A. Reid), and also at Moscow University (1968-69 with I.M.Gelfand). After a postdoc in Cambridge, she lectured at the Universities of York and Warwick, before taking up a position in SUNY, Stony Brook, USA in 1978. She moved to Barnard College in 2008.

Dietmar Salamon was born in Bremen, West Germany, in 1953. Studied Mathematics at the Universities of Hannover and Bremen from 1971 to 1978. PhD in Mathematics at the University of Bremen in 1982 under the supervision of Didi Hinrichsen. Postdoc positions at UW Madison and ETH Z urich from 1983 to 1986. Lecturer, Reader, and Professor at the University of Warwick from 1986 to 1998. Professor at ETH Zurich since 1998.

Introduction to Symplectic Topology

Third Edition

Dusa McDuff and Dietmar Salamon

Oxford Graduate Texts in Mathematics

Reviews and Awards

"A most welcome resource for graduate students entering the field... The book has been updated in many places, so that it also continues to serve as a reference work for specialists. The attentive reader will discover many other helpful details that have been added to this third edition." -- Hansjorg Geiges