Contact And Symplectic Topology PDF Download
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| Author | : Frédéric Bourgeois |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 538 |
| Release | : 2014-03-10 |
| Genre | : Science |
| ISBN | : 3319020366 |
Download Contact and Symplectic Topology Book in PDF, ePub and Kindle
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 | : Charles Benedict Thomas |
| Publisher | : Cambridge University Press |
| Total Pages | : 332 |
| Release | : 1996-09-28 |
| Genre | : Mathematics |
| ISBN | : 9780521570862 |
Download Contact and Symplectic Geometry Book in PDF, ePub and Kindle
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 |
| Total Pages | : 8 |
| Release | : 2008-03-13 |
| Genre | : Mathematics |
| ISBN | : 1139467956 |
Download An Introduction to Contact Topology Book in PDF, ePub and Kindle
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 | : David E. Blair |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475736045 |
Download Riemannian Geometry of Contact and Symplectic Manifolds Book in PDF, ePub and Kindle
Book endorsed by the Sunyer Prize Committee (A. Weinstein, J. Oesterle et. al.).
| 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 | : Robert Lipshitz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 279 |
| Release | : 2018-08-09 |
| Genre | : Floer homology |
| ISBN | : 1470428881 |
Download Bordered Heegaard Floer Homology Book in PDF, ePub and Kindle
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 | : Yakov Eliashberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 452 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780821886892 |
Download Symplectic Geometry and Topology Book in PDF, ePub and Kindle
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 | : 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 | : Franco Cardin |
| Publisher | : Springer |
| Total Pages | : 237 |
| Release | : 2014-12-01 |
| Genre | : Science |
| ISBN | : 3319110268 |
Download Elementary Symplectic Topology and Mechanics Book in PDF, ePub and Kindle
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 | : Chris Wendl |
| Publisher | : Springer |
| Total Pages | : 294 |
| Release | : 2018-06-28 |
| Genre | : Mathematics |
| ISBN | : 3319913719 |
Download Holomorphic Curves in Low Dimensions Book in PDF, ePub and Kindle
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
