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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On 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
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.
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This review is from: Introduction to Symplectic Topology (Oxford Mathematical Monographs) (Paperback)
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.The discussion begins with classic topology and cover a variety of final year undergraduate topics such as complex manifolds and inverse differential techniques before moving into the vastly complex world of Symplectic Topology. A must for researchers new to the field
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First Sentence:
Symplectic structures first arose in the study of classical mechanical systems such as the planetary system, and almost all the classical work on symplectic geometry was focused on the attempt to understand how these systems behave. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonsqueezing theorem, nonsqueezing property, unitary trivialization, symplectic trivialization, flux homomorphism, symplectic action functional, symplectic fibration, exact symplectic manifold, symplectic isotopy, symplectic spectrum, linear symplectomorphism, symplectic ball, variational family, symplectic cylinder, symplectic rigidity, symplectic complement, plectic topology, symplectic vector bundles, symplectic embeddings, symplectic bundle, coisotropic submanifold, symplectomorphism groups, neighbourhood theorem, symplectic connection, symplectic vector fields Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Symplectic structures first arose in the study of classical mechanical systems such as the planetary system, and almost all the classical work on symplectic geometry was focused on the attempt to understand how these systems behave. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonsqueezing theorem, nonsqueezing property, unitary trivialization, symplectic trivialization, flux homomorphism, symplectic action functional, symplectic fibration, exact symplectic manifold, symplectic isotopy, symplectic spectrum, linear symplectomorphism, symplectic ball, variational family, symplectic cylinder, symplectic rigidity, symplectic complement, plectic topology, symplectic vector bundles, symplectic embeddings, symplectic bundle, coisotropic submanifold, symplectomorphism groups, neighbourhood theorem, symplectic connection, symplectic vector fields Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 15
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34
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- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern in Back Matter (1), and Back Matter (2)
- Partial Differential Equations (Lectures in Applied Mathematics) by L. Bers in Back Matter
- Floer Memorial Volume (Progress in Mathematics) by Helmut Hofer in Back Matter
- Torus Actions on Symplectic Manifolds (Progress in Mathematics) by Michèle Audin in Back Matter
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter
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- Symplectic Geometry and Topology (Ias/Park City Mathematics Series, V. 7) by Yakov Eliashberg on 4 pages
- Symmetry in Mechanics by Stephanie Frank Singer on page 143, and Back Matter
- Handbook of Differential Equations: Ordinary Differential Equations, Volume 2 by A. Canada on page 145
- An Introduction to Invariants and Moduli by Shigeru Mukai in Back Matter
- The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein (Progress in Mathematics) by Jerrold E. Marsden on page 170
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