In particular he gave restrictions on the topology of a real projective variety birational to p3. If youre an algebraic geometer, i hope to give you a avour of some simple techniques in symplectic topology. Introduction to symplectic topology hardcover dusa. There is scope for progress on a wide range of questions, relating directly to other research topics. Introduction to symplectic topology oxford scholarship. Nondegeneracy and symplectic displacement energy 106 5. Symplectic capacities were introduced in 1990 by i. A symplectic form on a vector space v is a skewsymmetric bilinear form v. An introduction to symplectic geometry springerlink. Jholomorphic curves and symplectic topology 2nd dusa. American mathematical society colloquium publications volume 52 jholomorphic curves and symplectic topology second edition dusa mcduff dietmar. Introduction to symplectic topology oxford graduate texts. A symplectic form on v is a skewsymmetric bilinear nondegen.
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. 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. However, to rule out certain cases like hyperbolic or sol 3manifolds one needs techniques from symplectic geometry. The aim of this course is to present the recent work connecting sheaf theory and symplectic topology, due to several authors, nadler nad, nadz. Introduction to symplectic topology oxford mathematical. Introduction to symplectic topology dusa mcduff, dietmar. Salamon erratum to jholomorphic curves and symplectic topology ams 2004, last edited 21 april 2008, available in pdf. This second editionhas been significantly revised and expanded, with new references and examples added and theorems included or revised.
Recent developments in symplectic topology springerlink. Lectures on categorical dynamics and symplectic topology. Symplectic geometry has its origins in the hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes. As illustrated below, many of the quantitative aspects of symplectic geometry. An introduction to symplectic topology through sheaf theory. The first edition of introduction to symplectic topology was published in 1995.
Circle actions, which more appropriately means actions of the multiplicative group g g m. 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. Summer graduate program, introductory workshop, connections for women. Dec 14, 1995 symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior of a wide range of physical systems. Jholomorphic curves and symplectic topology 2nd dusa mcduff, dietmar salamon download bok. Dusa mcduff barnard mathematics department barnard college. Ny area symplectic topology seminar, columbia university. Symplectic structures a new approach to geometry dusa mcduff introduction symplectic geometry is the geometry of a closed skewsymmetric form. 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.
This is a collection of results on the topology of toric symplectic manifolds. Dusa mcduff barnard college, columbia university what is symplectic geometry. A symplectic form on v is a skewsymmetric bilinear nondegen erate form. These notes correct a few typos and errors in introduction to symplectic topology 2nd edition, oup 1998, reprinted 2005. Jholomorphic curves and symplectic topology pdf free. Prove that is symplectic if and only if its inverse is of the form 1 d t b tc at deduce that a 2 2 matrix is symplectic if and only if its determinant is equal to 1. Sep 29, 2014 the origins of symplectic topology lie in classical dynamics, and the search for periodic orbits of hamiltonian systems. Nowadays, symplectic geometry is a central field in mathematics with many. It turns out to be very different from the riemannian geometry with which we are familiar. The study of symplectic manifolds originated as an extension of classical. Symplectic capacities denote by v, co a symplectic vectorspace, i. A symplective vector space v is a pair of nite dimensional real vector space v. The origins of symplectic topology lie in classical dynamics, and the search for periodic orbits of hamiltonian systems.
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. Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds. For the past 30 years mcduff has been a contributor to the development of the field of symplectic geometry and topology. Pdf these notes are based on a week introductory course on symplectic and contact manifolds given by the senior. Introduction to symplectic topology, third edition, dusa mcduff and dietmar salamon oxford graduate texts inmathematics, 272017. 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. Cieliebak, introduction to symplectic geometry, part a and part b ver p agina. Professor mcduff is a leading authority in symplectic geometry. Salamon, introduction to symplectic topology, second.
Introduction to symplectic topology oxford graduate texts in. Salamon, introduction to symplectic topology, oxford mathematical mono. This second edition has been significantly revised and expanded, with new references and additional examples and theorems. 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. Cannas da silva, lectures on symplectic geometry, lecture notes in mathematics, 1764, springerverlag 2001. Dusa mcduff and dietmar salamon oxford graduate texts in mathematics. Holomorphic curves and quantum cohomology university lecture series 6 by dusa mcduff and dietmar s. Symplectic topology and algebraic geometry interact in many fruitful ways. Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior of a wide range of physical systems. 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. Pdf files can be viewed using adobe acrobat reader which can be. From dynamics to contact and symplectic topology and back. An introduction to symplectic geometry 3 we now turn to manifolds. Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some generalizations.
Salamon, introduction to symplectic topology, oup, oxford. Using an idea of borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. It is now understood to arise naturally in algebraic geometry, in lowdimensional topology, in representation theory and in string theory. C0symplectic topology and topologial hamiltonian dynamics 111 v. 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. At its publication in 1995, introduction to symplectic topology was the first comprehensive introduction to the subject, and has since become an established text in this fastdeveloping area of mathematics. An introduction to some concepts and open questions lecture 1. This does not mean that we are looking at gactions on symplectic manifolds which would be an entirely di erent topic. Symplectic topology explores the topological and geometric implications of the.
Salamon, introduction to symplectic topology, 3rd edition. Toric structures on bundles of projective spaces fanoe, andrew, journal of symplectic geometry, 2014. Holomorphic curves, planar open books and symplectic fillings. 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. Linear symplectic geometry symplectic vector spaces, the symplectic linear group, lagrangian subspaces, maslov index, complex structures 2. R is a skewsymmetric bilinear map and w p varies smoothly in p. Symplectic linear algebra let v be a real vector space. 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. Research networking programme contact and symplectic topology.
Research networking programme contact and symplectic. 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. Circle actions, quantum cohomology, and the fukaya category of. 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. Our task is made a little easier by the fact that symplectic topology was only born around 1983. Another exciting development is the introduction of sheaf. A significantly revised second edition was published in 1998 introducing new sections and updates on the fastdeveloping area.
Introduction to symplectic topology hardcover dusa mcduff. Pdf an introduction to symplectic and contact geometry. 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. Can be used as an introductory textbook for graduate students or mature mathematicians who are interested in symplectic topology but. Dusa mcduff and dietmar salamon, introduction to symplectic topology.
Salamon erratum to introduction to symplectic topology oup 1998 available in pdf recent survey articles. A new edition of this book will be available shortly. Typical applications so far include restrictions on the topology and intersection properties of certain classes of lagrangian embeddings in some symplectic manifolds. Yakov eliashberg stanford university symplectic topology of polynomial and rationally convexity jconvex functions and hypersurfaces a function. Salamon erratum to introduction to symplectic topology oup 1998 available in pdf.
This second edition has been significantly revised and expanded, with new references and examples added and theorems included or revised. She is a fellow of the american mathematical society, member of the national. The book was the first comprehensive introduction to the subject and became a key text in the area. We also include some additional clarifying material. Msri workshop schedules an introduction to symplectic. These arguments were provided by viterboeliashberg and welschingermangolte respectively. 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. Symplectic topology of polynomial and rationally convexity.