Symplectic And Contact Topology

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Lectures On Symplectic Geometry

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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27

Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.

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.

An Introduction To Contact Topology

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Author : Hansjörg Geiges
language : en
Publisher:
Release Date : 2014-05-14

An Introduction To Contact Topology written by Hansjörg Geiges and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.

The first comprehensive introduction to contact topology. Ideal for graduate courses on contact geometry, and as a reference for researchers.

Surgery On Contact 3 Manifolds And Stein Surfaces

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Author : Burak Ozbagci
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Surgery On Contact 3 Manifolds And Stein Surfaces written by Burak Ozbagci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Surfaces categories.

This book is about an investigation of recent developments in the field of sympletic and contact structures on four and three dimensional manifolds, respectively, from a topologist's point of view. The level of the book is appropriate for advanced graduate students.

A Brief Introduction To Symplectic And Contact Manifolds

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Author : Augustin Banyaga
language : en
Publisher: World Scientific
Release Date : 2016-08-08

A Brief Introduction To Symplectic And Contact Manifolds written by Augustin Banyaga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-08 with Mathematics categories.

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.

Symplectic Geometry And Topology

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Author : Yakov Eliashberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Symplectic Geometry And Topology written by Yakov Eliashberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Introduction To Symplectic Topology

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Author : Dusa McDuff
language : en
Publisher: Oxford University Press
Release Date : 2017

Introduction To Symplectic Topology written by Dusa McDuff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

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.

Bordered Heegaard Floer Homology

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Author : Robert Lipshitz
language : en
Publisher:
Release Date : 2018

Bordered Heegaard Floer Homology written by Robert Lipshitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Floer homology categories.

Symplectic And Contact Topology

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Author : Y. Eliashberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-01-01

Symplectic And Contact Topology written by Y. Eliashberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

The papers presented in this volume are written by participants of the ''Symplectic and Contact Topology, Quantum Cohomology, and Symplectic Field Theory'' symposium. The workshop was part of a semester-long joint venture of The Fields Institute in Toronto and the Centre de Recherches Mathematiques in Montreal. The twelve papers cover the following topics: Symplectic Topology, the interaction between symplectic and other geometric structures, and Differential Geometry and Topology. The Proceeding concludes with two papers that have a more algebraic character. One is related to the program of Homological Mirror Symmetry: the author defines a category of extended complex manifolds and studies its properties. The subject of the final paper is Non-commutative Symplectic Geometry, in particular the structure of the symplectomorphism group of a non-commutative complex plane. The in-depth articles make this book a useful reference for graduate students as well as research mathematicians.

An Introduction To Symplectic Geometry

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Author : Rolf Berndt
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-15

An Introduction To Symplectic Geometry written by Rolf Berndt and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-15 with Mathematics categories.

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.