Contact And Symplectic Topology

Author : Frédéric Bourgeois,Vincent Colin,András Stipsicz
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 46,9 Mb
Release : 2014-03-10
Category : Science
ISBN : 9783319020365

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Contact and Symplectic Topology by Frédéric Bourgeois,Vincent Colin,András Stipsicz Pdf

Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Author : Y. Eliashberg,Yakov Eliashberg,Boris A. Khesin,François Lalonde
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 44,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821831625

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Symplectic and Contact Topology: Interactions and Perspectives by Y. Eliashberg,Yakov Eliashberg,Boris A. Khesin,François Lalonde Pdf

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.

Author : Charles Benedict Thomas
Publisher : Cambridge University Press
Page : 332 pages
File Size : 44,5 Mb
Release : 1996-09-28
Category : Mathematics
ISBN : 0521570867

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Contact and Symplectic Geometry by Charles Benedict Thomas Pdf

This volume presents some of the lectures and research during the special programme held at the Newton Institute in 1994. The two parts each contain a mix of substantial expository articles and research papers that outline important and topical ideas. Many of the results have not been presented before, and the lectures on Floer homology is the first avaliable in book form.Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.

Author : Hansjörg Geiges
Publisher : Cambridge University Press
Page : 8 pages
File Size : 51,5 Mb
Release : 2008-03-13
Category : Mathematics
ISBN : 9781139467957

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An Introduction to Contact Topology by Hansjörg Geiges Pdf

This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 55,6 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 : David E. Blair
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 52,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475736045

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Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair Pdf

Book endorsed by the Sunyer Prize Committee (A. Weinstein, J. Oesterle et. al.).

Author : Robert Lipshitz,Peter Ozsváth,Dylan P. Thurston
Publisher : American Mathematical Soc.
Page : 279 pages
File Size : 46,9 Mb
Release : 2018-08-09
Category : Floer homology
ISBN : 9781470428884

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Bordered Heegaard Floer Homology by Robert Lipshitz,Peter Ozsváth,Dylan P. Thurston Pdf

The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

Author : Dusa McDuff,Dietmar Salamon
Publisher : Oxford University Press
Page : 637 pages
File Size : 40,8 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 : Yakov Eliashberg,Lisa M. Traynor
Publisher : American Mathematical Soc.
Page : 452 pages
File Size : 50,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0821886894

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Symplectic Geometry and Topology by Yakov Eliashberg,Lisa M. Traynor Pdf

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.

Author : Anahita Eslami Rad
Publisher : Springer Nature
Page : 185 pages
File Size : 52,8 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9783031562259

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Symplectic and Contact Geometry by Anahita Eslami Rad Pdf

Author : Franco Cardin
Publisher : Springer
Page : 222 pages
File Size : 47,6 Mb
Release : 2014-12-01
Category : Science
ISBN : 9783319110264

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Elementary Symplectic Topology and Mechanics by Franco Cardin Pdf

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Author : Dusa McDuff,Dietmar Salamon
Publisher : American Mathematical Soc.
Page : 744 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821887462

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J-holomorphic Curves and Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

Author : Chris Wendl
Publisher : Springer
Page : 294 pages
File Size : 43,6 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9783319913711

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Holomorphic Curves in Low Dimensions by Chris Wendl Pdf

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

Author : Augustin Banyaga,Djideme F Houenou
Publisher : World Scientific
Page : 180 pages
File Size : 45,8 Mb
Release : 2016-08-08
Category : Electronic
ISBN : 9789814696722

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A Brief Introduction to Symplectic and Contact Manifolds by Augustin Banyaga,Djideme F Houenou Pdf

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. Contents: Symplectic Vector SpacesSymplectic ManifoldsHamiltonian Systems and Poisson AlgebraGroup ActionsContact ManifoldsSolutions of Selected ExercisesEpilogue: The C0-Symplectic and Contact Topology Readership: Graduate students, researchers and more advanced mathematicians. Symplectic;Contact GeometryKey Features: It is briefThe easy part has been tested and been used for a short courseThe advanced material develops things related to one of the author's research furtherThere is no book, going from the very elementary part to the very advanced level, like this one

Author : Bahar Acu,Catherine Cannizzo,Dusa McDuff,Ziva Myer,Yu Pan,Lisa Traynor
Publisher : Springer Nature
Page : 341 pages
File Size : 42,8 Mb
Release : 2022-02-02
Category : Mathematics
ISBN : 9783030809799

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Research Directions in Symplectic and Contact Geometry and Topology by Bahar Acu,Catherine Cannizzo,Dusa McDuff,Ziva Myer,Yu Pan,Lisa Traynor Pdf

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field. The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors included female and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work.