Function Theory On Symplectic Manifolds PDF Download
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Author | : Leonid Polterovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2014 |
Genre | : Geometric function theory |
ISBN | : 147041693X |
Download Function Theory on Symplectic Manifolds Book in PDF, ePub and Kindle
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 | : Ana Cannas da Silva |
Publisher | : Springer |
Total Pages | : 240 |
Release | : 2004-10-27 |
Genre | : Mathematics |
ISBN | : 354045330X |
Download Lectures on Symplectic Geometry Book in PDF, ePub and Kindle
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 | : Jacques Hurtubise |
Publisher | : Springer Science & Business Media |
Total Pages | : 227 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401716676 |
Download Gauge Theory and Symplectic Geometry Book in PDF, ePub and Kindle
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 | : Augustin Banyaga |
Publisher | : World Scientific |
Total Pages | : 178 |
Release | : 2016-08-08 |
Genre | : Mathematics |
ISBN | : 9814696722 |
Download A Brief Introduction To Symplectic And Contact Manifolds Book in PDF, ePub and Kindle
The book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.The book contains also more advanced material, suitable to advanced graduate students and researchers.
Author | : R.E. Greene |
Publisher | : Springer |
Total Pages | : 219 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540355367 |
Download Function Theory on Manifolds Which Possess a Pole Book in PDF, ePub and Kindle
Author | : Alesky Tralle |
Publisher | : Springer |
Total Pages | : 216 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540691456 |
Download Symplectic Manifolds with no Kaehler structure Book in PDF, ePub and Kindle
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 | : Michèle Audin |
Publisher | : Birkhäuser |
Total Pages | : 181 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034872216 |
Download The Topology of Torus Actions on Symplectic Manifolds Book in PDF, ePub and Kindle
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 |
Publisher | : Oxford University Press |
Total Pages | : 637 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 0198794894 |
Download Introduction to Symplectic Topology Book in PDF, ePub and Kindle
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 | : Anahita Eslami Rad |
Publisher | : Springer Nature |
Total Pages | : 185 |
Release | : |
Genre | : |
ISBN | : 3031562259 |
Download Symplectic and Contact Geometry Book in PDF, ePub and Kindle
Author | : Alan Weinstein |
Publisher | : American Mathematical Soc. |
Total Pages | : 58 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : 0821816799 |
Download Lectures on Symplectic Manifolds Book in PDF, ePub and Kindle
Features notes with sections containing a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. This title also includes sections dealing with various aspects of the quantization problem, as wel as those giving a feedback of ideas from quantization theory into symplectic geometry itslef.