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Introduction to Symplectic Topology (Oxford Mathematical Monographs)

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Introduction to Symplectic Topology (Oxford Mathematical Monographs) Cover

 

Synopses & Reviews

Publisher Comments:

Symplectic structures underlie the equations of classical mechanics, and their properties are reflected in the behavior of a wide range of physical systems. Over the years much detailed information has accumulated about the behavior of particular systems. Powerful new methods, such as Gromov's flexibility theorem and proofs of the Arnold conjectures, have produced striking results, but the modern global theory of symplectic topology has only recently emerged. This book is an introduction to the subject for postgraduate students, presenting new methods in the field and providing proofs of the simpler versions of the most important new theorems. The deepest theorems in the book are proved by a new finite dimensional variational analysis which combines ideas from Viterbo's generating function approach with the infinite dimensional variational analysis of Hofer-Zehnder. Exercises are also included.

Synopsis:

Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior 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 it has since become an established text in this fast-developing branch of mathematics. This second edition has been significantly revised and expanded, with new references and additional examples and theorems. It includes a section on new developments and an expanded discussion of Taubes and Donaldson's recent results.

Description:

Includes bibliographical references (p. [458]-471) and index.

About the Author

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.

Table of Contents

Introduction

I. FOUNDATIONS

1. From classical to modern

2. Linear symplectic geometry

3. Symplectic manifolds

4. Almost complex structures

II. SYMPLECTIC MANIFOLDS

5. Symplectic group actions

6. Symplectic Fibrations

7. Constructing Symplectic Manifolds

III. SYMPLECTOMORPHISMS

8. Area-preserving diffeomorphisms

9. Generating functions

10. The group of symplectomorphisms

IV. SYMPLECTIC INVARIANTS

11. The Arnold conjecture

12. Symplectic capacities

13. New directions

References

Index

Product Details

ISBN:
9780198504511
Preface:
Salamon, Dietmar
Preface:
Salamon, Dietmar
Preface by:
Salamon, Dietmar
Preface:
Salamon, Dietmar
Author:
null, Dusa
Author:
Salamon, Dietmar
Author:
null, Dietmar
Author:
McDuff, Dusa
Author:
Salamon, Dietmar
Publisher:
Oxford University Press, USA
Location:
Oxford
Subject:
Mathematics
Subject:
Geometry - Differential
Subject:
Topology
Subject:
Symplectic manifolds
Subject:
Topology - General
Subject:
Mathematics | Pure Mathematics
Subject:
MATHEMATICS / Topology
Edition Number:
2
Series:
Oxford Mathematical Monographs
Series Volume:
52-5
Publication Date:
19980931
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
43 line illus
Pages:
496
Dimensions:
6 x 8.9 x 1.1 in 1.663 lb

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Introduction to Symplectic Topology (Oxford Mathematical Monographs) New Trade Paper
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Product details 496 pages Oxford University Press - English 9780198504511 Reviews:
"Synopsis" by , Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior 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 it has since become an established text in this fast-developing branch of mathematics. This second edition has been significantly revised and expanded, with new references and additional examples and theorems. It includes a section on new developments and an expanded discussion of Taubes and Donaldson's recent results.
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