Jun 14, 2017 kylerec on jholomorphic curves, part 1 this tobe2partbecausethisgotlong post is a continuation of the series on kylerec 2017 starting with the previous post, and covers most of the talks from days 23 of kylerec, focusing on the use of jholomorphic curves in the study of fillings. Since their introduction by gromov 4 in the mid1980s jholomorphic curves have been one of the most widely used tools in symplectic geometry, leading to the formulation of various theories gromovwitten invariants, quantum cohomology, various floer homologies, symplectic field theory, fukaya category, answers to old questions in symplectic geometry various arnold. Jholomorphic curves and symplectic topology by dusa mcduff. S v where s is a riemannian surface passing through v, such that the symplectic area off satisfies f co download fulltext pdf. The theory of jholomorphic curves has been of great importance to symplectic topologists ever since its inception in gromovs paper 26 of 1985.
Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in hamiltons equation. Symplectic topology is a subfield of symplectic geometry, in which global properties of symplectic. Intersection multiplicities of holomorphic and algebraic curves with divisors. Kylerec on jholomorphic curves, part 1 the electric. In mathematics, specifically in topology and geometry, a pseudoholomorphic curve or jholomorphic curve is a smooth map from a riemann surface into an almost complex manifold that satisfies the cauchyriemann equation. Jholomorphic curves and symplectic topology 2nd dusa mcduff, dietmar salamon download bok. The moduli space of these curves called pesudoholomorphic curves is typically noncompact and not wellbehaved. Jholomorphic curves and symplectic topology mathematical.
Jholomorphic curves and quantum cohomology dusa mcduff, dietmar salamon download bok. Singularities and positivity of intersections of jholomorphic curves. In mathematical physics, it provides a natural context in which to define gromovwitten invariants and quantum cohomology, two important ingredients of the mirror symmetry conjecture. Jholomorphic curves and gromovwitten invariants icts. Jholomorphic curves and symplectic topology dusa mcduff. The present book started life as a second edition of that book, but the project quickly grew. Its applications include many key results in symplectic topology. Books here is the revised 1995 text of the book jholomorphic curves and quantum homology ams lecture notes, 1994 that i wrote with salamon. J holomorphic curves in symplectic topology manabu akaho. Applications of pseudoholomorphic curves to symplectic topology. Get your kindle here, or download a free kindle reading app. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Differential and symplectic topology of knots and curves. Holomorphic curves in symplectic geometry it seems that youre in usa.
Jholomorphic curves and symplectic invariants springerlink. This is explained for example in mcduffsalomons j holomorphic curves in symplectic topology, in one of the first sections. Symplectic geometry on moduli spaces of jholomorphic curves j. Differential geometry symplectic geometry, contact geometry gromovwitten invariants, quantum cohomology, frobenius manifolds. This is explained for example in mcduffsalomons jholomorphic curves in symplectic topology, in one of the first sections. Introduction applications of pseudoholomorphic curves to symplectic topology. Freecourseweb jholomorphic curves and symplectic topology, 2nd edition. Jholomorphic curves and symplectic topology semantic scholar. Symplectic geometry on moduli spaces of jholomorphic curves. The theory of jholomorphic curves has been of great importance since its introduction by gromov in 1985. Almost complex manifolds and jholomorphic curves 25 2.
Lectures on holomorphic curves in symplectic and contact geometry. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. We outline the construction of invariants of hamiltonian group actions on symplectic manifolds. This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at eth zurich and the humboldt university berlin in 20092010. Jholomorphic curves and symplectic topology in searchworks. Here is the revised 1995 text of the book j holomorphic curves and quantum homology ams lecture notes, 1994 that i wrote with salamon. Abstract let m be a symplectic manifold, and a compact riemann surface. One might wonder why we care about these objects, and the rest of this post along with part 2 should be a testament to some but certainly not all aspects of the power. Hyperbolic embeddedness and extensionconvergence theorems of jholomorphic curves.
Jholomorphic curves and symplectic topology pdf free download. Gromov introduced the study of jholomorphic curves into symplectic geometry in his famous 1985 paper, immediately revolutionizing the field. It contains a few mistakes and many omissions which are detailed in this commentary of october 2007. Nov 07, 2010 this is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at eth zurich and the humboldt university berlin in 20092010. I also mentioned that for compatible j, the symplectic form is a calibration, so that jcurves are conformal parametrizations of absolutely areaminimizing surfaces. Keywords moduli space symplectic form j holomorphic curve almost complex structure. Lectures on pseudo holomorphic curves and the symplectic isotopy problem bernd siebert and gang tian abstract.
In mathematics, specifically in topology and geometry, a pseudoholomorphic curve or jholomorphic curve. Singularities and positivity of intersections of jholomorphic. Jholomorphic curves and quantum cohomology people eth. Given an almost complex structure j on a manifold m, a map f from a riemann surface to m is called a pseudoholomorphic or jholomorphic curve if at each point p of the surface, the ordinary differential is a complex linear map with respect to the complex structures jp and jfp on tangent spaces. Download torrent topology fast and easy torrent search. Jholomorphic curves and symplectic topology dusa mcduff, dietmar salamon download bok. It was also one of the main inspirations for the creation of floer homology. Our definition of super jholomorphic curve allows to generalize those results. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase. Jholomorphic curves and symplectic topology pdf free. All in all jholomorphic curves and symplectic topology is a scholarly work of great pedagogical value, and an evident sine quo non for entry into the subject of symplectic topology and the hot areas of research it generates and touches. A nice compactification, due to gromov, allows us to define certain invariants known as gromovwitten invariants.
In these lectures, we present the basic results on the theory of. Almost complex manifolds and jholomorphic curves 23 2. Compatible and tame almost complex structures 29 2. Holomorphic curves in symplectic geometry michele audin. I also mentioned that for compatible j, the symplectic form is a calibration, so that j curves are conformal parametrizations of absolutely areaminimizing surfaces. But avoid asking for help, clarification, or responding to other answers. Introduction symplectic topology is renowned for its invariants which are either incomputable or only conjecturally wellde ned. Jholomorphic curves and symplectic topology request pdf. This content was uploaded by our users and we assume good faith they have the permission to share this book. From symplectic geometry to symplectic topology 10 1. Jholomorphic curves and symplectic topology 2nd american mathematical society.
In particular, we deduce sufficient conditions for the existence of jholomorphic. In mathematics, its applications include many key results in symplectic topology. Jholomorphic curves and symplectic topology by dusa. The theory of \ j\ holomorphic curves has been of great importance since its introduction by gromov in 1985. The theory of j holomorphic curves has been of great importance since its introduction by gromov in 1985. In particular if it is a closed curve it is minimizing in its homology class. You can help us by sharing the link with friends, in social networks, message boards and other mass media.
It is related to the theory of dynamical systems and via holomorphic curves to algebraic geometry. But be forewarned, serious commitment is required from the reader and rightly so, of course. Citeseerx jholomorphic curves in symplectic geometry. In mathematical physics, it provides a natural context in which to define gromovwitten invariants and quantum cohomologytwo important ingredients of the mirror symmetry conjecture. Differential geometry symplectic geometry, contact geometry symplectic manifolds, general. Lectures on pseudoholomorphic curves and the symplectic isotopy problem bernd siebert and gang tian abstract. Given an almost complex structure j on a manifold m, a map f from a riemann surface to m is called a pseudoholomorphic or j holomorphic curve if at each point p of the surface, the ordinary differential is a complex linear map with respect to the complex structures j p and j fp on tangent spaces.
Jholomorphic curves and symplectic topology 2nd dusa. The purpose of these notes is a more selfcontained presentation of the results of the authors in siti3. The notes are still incomplete, but due to recent requests from readers, ive decided to make a presentable halffinished version available here. Introduced in 1985 by mikhail gromov, pseudoholomorphic curves have since revolutionized the study of symplectic manifolds. Holomorphic curves in symplectic geometry springerlink. Lagrangian intersections, symplectic energy, and areas. Lectures on holomorphic curves in symplectic and contact. Its mathematical applications include many key results in symplectic topology. Jholomorphic curves and quantum cohomology dusa mcduff and. Jholomorphic curves and quantum cohomology dusa mcduff. Thanks for contributing an answer to mathematics stack exchange. The fate of our site directly depends on its relevance. On finiteness and rigidity of jholomorphic curves in.
447 604 1271 872 995 1525 41 728 1185 30 512 1072 1163 813 298 1262 1612 1237 603 1226 168 231 781 400 1069 210 381 1476 1605 1334 1630 595 571 1408 574 868 486 1279 76