Function Theory On Symplectic Manifolds

Author : Leonid Polterovich,Daniel Rosen
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 54,8 Mb
Release : 2014
Category : Geometric function theory
ISBN : 9781470416935

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Function Theory on Symplectic Manifolds by Leonid Polterovich,Daniel Rosen Pdf

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.

Author : Jacques Hurtubise,François Lalonde
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 41,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401716673

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Gauge Theory and Symplectic Geometry by Jacques Hurtubise,François Lalonde Pdf

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 43,9 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Author : Alan Weinstein
Publisher : American Mathematical Soc.
Page : 48 pages
File Size : 47,9 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821816790

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Lectures on Symplectic Manifolds by Alan Weinstein Pdf

The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.

Author : Michèle Audin
Publisher : Birkhäuser
Page : 181 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034872218

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The Topology of Torus Actions on Symplectic Manifolds by Michèle Audin Pdf

The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 47,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198794899

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

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. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.

Author : Carl H. FitzGerald,Sheng Gong
Publisher : World Scientific
Page : 360 pages
File Size : 55,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9812702504

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Geometric Function Theory in Several Complex Variables by Carl H. FitzGerald,Sheng Gong Pdf

The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Author : R.E. Greene,H. Wu
Publisher : Springer
Page : 219 pages
File Size : 55,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540355366

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Function Theory on Manifolds Which Possess a Pole by R.E. Greene,H. Wu Pdf

Author : R. E. Greene,H. Wu
Publisher : Unknown
Page : 228 pages
File Size : 46,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662183935

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Function Theory on Manifolds Which Possess a Pole by R. E. Greene,H. Wu Pdf

Author : S. K. Donaldson,Charles Benedict Thomas
Publisher : Cambridge University Press
Page : 264 pages
File Size : 40,7 Mb
Release : 1990
Category : Low-dimensional topology
ISBN : 0521400015

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Symplectic Manifolds and Jones-Witten Theory by S. K. Donaldson,Charles Benedict Thomas Pdf

Author : Robert Everist Greene,Hongxi Wu,Hung-hsi Wu
Publisher : Springer
Page : 213 pages
File Size : 41,9 Mb
Release : 1979
Category : Complex manifolds
ISBN : 0387091084

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Function Theory on Manifolds which Possess a Pole by Robert Everist Greene,Hongxi Wu,Hung-hsi Wu Pdf

Author : Alesky Tralle,John Oprea
Publisher : Springer
Page : 216 pages
File Size : 50,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540691457

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Symplectic Manifolds with no Kaehler structure by Alesky Tralle,John Oprea Pdf

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.

Author : Albert Fathi,Yong-Geun Oh,Claude Viterbo
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 50,8 Mb
Release : 2010-04-09
Category : Mathematics
ISBN : 9780821848920

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Symplectic Topology and Measure Preserving Dynamical Systems by Albert Fathi,Yong-Geun Oh,Claude Viterbo Pdf

The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.

Author : Rolf Berndt
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 42,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0821820567

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An Introduction to Symplectic Geometry by Rolf Berndt Pdf

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 632 pages
File Size : 50,8 Mb
Release : 2017-03-16
Category : Mathematics
ISBN : 9780192514011

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Introduction to Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

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.