Holomorphic curves and quantum cohomology university lecture series 6 by dusa mcduff and dietmar s. Symplectic and contact structures first arose in the study of classical mechanical systems, allowing one to describe the time evolution of both simple and complex. Symplectic capacities were introduced in 1990 by i. She is a fellow of the american mathematical society, member of the national. Summer graduate program, introductory workshop, connections for women. We also include some additional clarifying material.
Introduction to symplectic topology hardcover dusa mcduff. Linear symplectic geometry symplectic vector spaces, the symplectic linear group, lagrangian subspaces, maslov index, complex structures 2. Ny area symplectic topology seminar, columbia university. An introduction to symplectic geometry 3 we now turn to manifolds. A symplectic form on v is a skewsymmetric bilinear nondegen erate form. Yakov eliashberg stanford university symplectic topology of polynomial and rationally convexity jconvex functions and hypersurfaces a function. Introduction to symplectic topology oxford graduate texts. Recent developments in symplectic topology springerlink. A symplective vector space v is a pair of nite dimensional real vector space v. Cannas da silva, lectures on symplectic geometry, lecture notes in mathematics, 1764, springerverlag 2001. An introduction to some concepts and open questions lecture 1. The book was the first comprehensive introduction to the subject and became a key text in the area.
Symplectic capacities denote by v, co a symplectic vectorspace, i. Salamon erratum to introduction to symplectic topology oup 1998 available in pdf. Salamon erratum to jholomorphic curves and symplectic topology ams 2004, last edited 21 april 2008, available in pdf. The origins of symplectic topology lie in classical dynamics, and the search for periodic orbits of hamiltonian systems. However, to rule out certain cases like hyperbolic or sol 3manifolds one needs techniques from symplectic geometry. Salamon, introduction to symplectic topology, second. Holomorphic curves, planar open books and symplectic fillings. Over the last few 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. Introduction to symplectic topology oxford graduate texts in. Introduction to symplectic topology oxford mathematical. The study of symplectic manifolds originated as an extension of classical. This second edition has been significantly revised and expanded, with new references and examples added and theorems included or revised. This is a collection of results on the topology of toric symplectic manifolds. Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some generalizations.
American mathematical society colloquium publications volume 52 jholomorphic curves and symplectic topology second edition dusa mcduff dietmar. Another exciting development is the introduction of sheaf. Sep 29, 2014 the origins of symplectic topology lie in classical dynamics, and the search for periodic orbits of hamiltonian systems. A new edition of this book will be available shortly. Symplectic geometry has its origins in the hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes. It turns out to be very different from the riemannian geometry with which we are familiar. At its publication in 1995, introduction to symplectic topology was the first comprehensive introduction to the subject and it has since become an established text in this fastdeveloping branch of mathematics. In particular he gave restrictions on the topology of a real projective variety birational to p3. An introduction to symplectic geometry springerlink. An introduction to symplectic topology through sheaf theory.
Cieliebak, introduction to symplectic geometry, part a and part b ver p agina. R is a skewsymmetric bilinear map and w p varies smoothly in p. Salamon erratum to introduction to symplectic topology oup 1998 available in pdf recent survey articles. Pdf an introduction to symplectic and contact geometry. Symplectic geometry has its origins in the hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic. Can be used as an introductory textbook for graduate students or mature mathematicians who are interested in symplectic topology but. Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds. Salamon, introduction to symplectic topology, oxford mathematical mono. Symplectic topology explores the topological and geometric implications of the. Introduction to symplectic topology oxford scholarship.
Symplectic topology of polynomial and rationally convexity. For the past 30 years mcduff has been a contributor to the development of the field of symplectic geometry and topology. Understanding the evolution and distinguishing transformations of these systems led to the development of global invariants of symplectic and contact manifolds. One important difference is that, although all its concepts are initially expressed in. Jholomorphic curves and symplectic topology 2nd dusa. Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior of a wide range of physical systems. Circle actions, quantum cohomology, and the fukaya category of. Dusa mcduff barnard college, columbia university what is symplectic geometry. Symplectic and contact structures first arose in the study of classical mechanical systems, allowing one to describe the time evolution of both simple and complex systems such as springs, planetary motion, and wave propagation. There is scope for progress on a wide range of questions, relating directly to other research topics. Dusa mcduff barnard mathematics department barnard college. Symplectic structures a new approach to geometry dusa mcduff introduction symplectic geometry is the geometry of a closed skewsymmetric form. Circle actions, which more appropriately means actions of the multiplicative group g g m. Typical applications so far include restrictions on the topology and intersection properties of certain classes of lagrangian embeddings in some symplectic manifolds.
Dusa mcduff and dietmar salamon, introduction to symplectic topology. This second edition has been significantly revised and expanded, with new references and additional examples and theorems. Pdf files can be viewed using adobe acrobat reader which can be. August 10, 2009 7 views about 7 years ago show more videos msri has been supported from its originsby the national science foundation,now joined by the national security agency,over 100 academic sponsor departments,by a range of private foundations,and by generous. A significantly revised second edition was published in 1998 introducing new sections and updates on the fastdeveloping area. Anintroductiontoliegroups andsymplecticgeometry a series of nine lectures on lie groups and symplectic geometry delivered at the regional geometry institute in park city, utah, 24 june20 july 1991. Lectures on categorical dynamics and symplectic topology. Introduction symplectic and contact topology is an active area of mathematics that combines ideas from dynamical systems, analysis, topology, several complex variables, and differential and algebraic geometry. Over the past 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.
Professor mcduff is a leading authority in symplectic geometry. Introduction to symplectic topology hardcover dusa. Nowadays, symplectic geometry is a central field in mathematics with many. Can be used as an introductory textbook for graduate students or mature mathematicians who are interested in symplectic topology but are as yet unfamiliar with the subject. Introduction to symplectic topology dusa mcduff, dietmar. She gave the first example of symplectic forms on a closed manifold that are cohomologous but not diffeomorphic and also classified the rational and ruled symplectic fourmanifolds, completed with francois lalonde. We call a linear map t 9 lv symplectic if it preserves co, that is cox, y co tx, ty for every x, y 9 v.
Jholomorphic curves and symplectic topology 2nd dusa mcduff, dietmar salamon download bok. Symplectic linear algebra let v be a real vector space. The aim of this course is to present the recent work connecting sheaf theory and symplectic topology, due to several authors, nadler nad, nadz. Toric structures on bundles of projective spaces fanoe, andrew, journal of symplectic geometry, 2014. Nondegeneracy and symplectic displacement energy 106 5. From dynamics to contact and symplectic topology and back. If youre an algebraic geometer, i hope to give you a avour of some simple techniques in symplectic topology. Salamon, introduction to symplectic topology, 3rd edition. Research networking programme contact and symplectic topology. A symplectic form on a vector space v is a skewsymmetric bilinear form v.
This second editionhas been significantly revised and expanded, with new references and examples added and theorems included or revised. An introduction to symplectic geometry megumi harada, lecture notes by kaname hashimoto summer school, osaka, 2007 abstract the intent of this series of lectures is twofold. Jholomorphic curves and symplectic topology pdf free. This does not mean that we are looking at gactions on symplectic manifolds which would be an entirely di erent topic.
Symplectic topology and algebraic geometry interact in many fruitful ways. The first edition of introduction to symplectic topology was published in 1995. As illustrated below, many of the quantitative aspects of symplectic geometry. Using an idea of borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Dusa mcduff and dietmar salamon oxford graduate texts in mathematics. C0symplectic topology and topologial hamiltonian dynamics 111 v. Holomorphic curves, planar open books and symplectic fillings a minicourse by chris wendl the overarching theme of this minicourse will be the properties of pseudoholomorphic curves and their use in proving global results about symplectic or contact manifolds based on more localized information. Pdf these notes are based on a week introductory course on symplectic and contact manifolds given by the senior.
693 138 1405 11 136 1385 363 956 146 293 1192 549 836 1667 979 335 379 562 1454 1223 1304 271 309 1014 431 259 1399 1333 344 1322 80 641 47 1140 83 451 698 177 1391 715 1319 90 625