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Function Theory on Symplectic Manifolds

Leonid Polterovich Tel Aviv University, Tel Aviv, Israel
Daniel Rosen Tel Aviv University, Israel
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Hardcover ISBN: 978-1-4704-1693-5
Product Code: CRMM/34
List Price: $96.00 MAA Member Price:$86.40
AMS Member Price: $76.80 Electronic ISBN: 978-1-4704-1931-8 Product Code: CRMM/34.E List Price:$90.00
MAA Member Price: $81.00 AMS Member Price:$72.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $144.00 MAA Member Price:$129.60
AMS Member Price: $115.20 Click above image for expanded view Function Theory on Symplectic Manifolds Leonid Polterovich Tel Aviv University, Tel Aviv, Israel Daniel Rosen Tel Aviv University, Israel A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Hardcover ISBN: 978-1-4704-1693-5 Product Code: CRMM/34  List Price:$96.00 MAA Member Price: $86.40 AMS Member Price:$76.80
 Electronic ISBN: 978-1-4704-1931-8 Product Code: CRMM/34.E
 List Price: $90.00 MAA Member Price:$81.00 AMS Member Price: $72.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$144.00 MAA Member Price: $129.60 AMS Member Price:$115.20
• Book Details

CRM Monograph Series
Volume: 342014; 203 pp
MSC: Primary 53; Secondary 57; 81; 22; 20; 28;

This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is important and interesting.

Dusa McDuff, Barnard College, Columbia University

This is a very important book, coming at the right moment. The book is a remarkable mix of introductory chapters and research topics at the very forefront of actual research. It is full of cross fertilizations of different theories, and will be useful to Ph.D. students and researchers in symplectic geometry as well as to many researchers in other fields (geometric group theory, functional analysis, mathematical quantum mechanics). It is also perfectly suited for a Ph.D.-students seminar.

Felix Schlenk, Université de Neuchâtel

Graduate students and research mathematicians interested in symplectic geometry/topology, Hamiltonian dynamics, and quantum mechanics.

• Chapters
• Three wonders of symplectic geometry
• $C^0$-rigidity of the Poisson bracket
• Quasi-morphisms
• Symplectic quasi-states and quasi-measures
• Applications of partial symplectic quasi-states
• A Poisson bracket invariant of quadruples
• Symplectic approximation theory
• Geometry of covers and quantum noise
• Preliminaries from Morse theory
• An overview of Floer theory

• Reviews

• Yakov Eliashberg
• The intervening chapters, connecting the first chapter's discussion of these 'wonders' to the exciting stuff mentioned above, is concerned with a lot of heavy machinery, but it's all presented in a streamlined fashion: quasi-morphisms, spectral invariants, and symplectic approximation theory make an appearance, for example. [It] is very exciting and deep mathematics: it's really altogether irresistible.

MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 342014; 203 pp
MSC: Primary 53; Secondary 57; 81; 22; 20; 28;

This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is important and interesting.

Dusa McDuff, Barnard College, Columbia University

This is a very important book, coming at the right moment. The book is a remarkable mix of introductory chapters and research topics at the very forefront of actual research. It is full of cross fertilizations of different theories, and will be useful to Ph.D. students and researchers in symplectic geometry as well as to many researchers in other fields (geometric group theory, functional analysis, mathematical quantum mechanics). It is also perfectly suited for a Ph.D.-students seminar.

Felix Schlenk, Université de Neuchâtel

Graduate students and research mathematicians interested in symplectic geometry/topology, Hamiltonian dynamics, and quantum mechanics.

• Chapters
• Three wonders of symplectic geometry
• $C^0$-rigidity of the Poisson bracket
• Quasi-morphisms
• Symplectic quasi-states and quasi-measures
• Applications of partial symplectic quasi-states
• A Poisson bracket invariant of quadruples
• Symplectic approximation theory
• Geometry of covers and quantum noise
• Preliminaries from Morse theory
• An overview of Floer theory