Singularities and positivity of intersections of jholomorphic curves. Lectures on holomorphic curves in symplectic and contact. Almost complex manifolds and jholomorphic curves 25 2. Jholomorphic curves and symplectic topology in searchworks. This site is like a library, you could find million book here by using search box in the.
Request pdf on jan 1, 2004, dusa mcduff and others published j holomorphic curves and symplectic topology find, read and cite all the research you need on researchgate. 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. These two propertiesthe fredholm theory and compactnesslay the foundations for gromovs theory, in which the pseudoholomorphic curves are used as a tool in symplectic topology. Abstract let m be a symplectic manifold, and a compact riemann surface. Request pdf on jan 1, 2004, dusa mcduff and others published jholomorphic curves and symplectic topology find, read and cite all the research you need on researchgate. The theory of j holomorphic curves has been of great importance since its introduction by gromov in 1985. Almost complex manifolds and j holomorphic curves 25 2. 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. Click download or read online button to get topology illustrated book now.
Holomorphic curves in symplectic geometry michele audin. S i on the space s i of immersed symplectic surfaces in m, and show that the form is closed and nondegenerate, up to reparametrizations. Jholomorphic curves and symplectic topology by dusa mcduff. Almost complex manifolds and jholomorphic curves 23 2. Symplectic topology and floer homology by yonggeun oh. Holomorphic curves in symplectic geometry springerlink. By a theorem of gromov, for an almost complex structure j on c p 2 tamed by the standard symplectic structure, the jholomorphic curves representing the positive generator of homology form a projective plane. Differential geometry symplectic geometry, contact geometry symplectic manifolds, general. This is explained for example in mcduffsalomons jholomorphic curves in symplectic topology, in one of the first sections. The aim of this course is to present the recent work connecting sheaf theory and symplectic topology, due to several authors, nadler nad, nadz. This content was uploaded by our users and we assume good faith they have the permission to share this book. The theory of jholomorphic curves has been of great importance to symplectic topologists ever since its inception in gromovs paper 26 of 1985. Differential and symplectic topology of knots and curves.
Lectures on holomorphic curves in symplectic and contact geometry work in progressversion 3. An introduction to symplectic topology through sheaf theory. Topology illustrated download ebook pdf, epub, tuebl, mobi. From symplectic geometry to symplectic topology 10 1. I also mentioned that for compatible j, the symplectic form is a calibration, so that j curves are conformal parametrizations of absolutely areaminimizing surfaces.
Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. Jholomorphic curves and symplectic topology dusa mcduff, dietmar salamon download bok. The existence of global symplectic geometry was first to authors knowledge. Jholomorphic curves and symplectic topology 2nd dusa mcduff, dietmar salamon download bok. Lectures on holomorphic curves in symplectic and contact geometry. I also mentioned that for compatible j, the symplectic form is a calibration, so that jcurves are conformal parametrizations of absolutely areaminimizing surfaces. Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in hamiltons equation. Applications of pseudoholomorphic curves to symplectic topology. Let j be an almost complex structure on c p 2 that is tamed by the standard symplectic structure, i. Jholomorphic curves and symplectic topology second. Jholomorphic curves and quantum cohomology dusa mcduff, dietmar salamon download bok.
J holomorphic curves and symplectic topology 2nd dusa mcduff, dietmar salamon download bok. Lafontaine, editors, progress in math 117, birkhauser 1994 233250. J holomorphic curves in symplectic topology manabu akaho. Mcduffsalamons book jholomorphic curves and symplectic topology, second edition. T parker, j wolfson, pseudoholomorphic maps and bubble trees, journ. It was also one of the main inspirations for the creation of floer homology. Jholomorphic curves and symplectic topology pdf free download. All books are in clear copy here, and all files are secure so dont worry about it. Pseudo holomorphic curves in symplectic manifolds ihes. This site is like a library, use search box in the widget to get ebook that you want. Moduli of jholomorphic curves with lagrangian boundary. 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. In mathematics, its applications include many key results in symplectic topology.
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. Download topology illustrated or read online books in pdf, epub, tuebl, and mobi format. The theory of \ j \ holomorphic curves has been of great importance since its introduction by gromov in 1985. In order to compactify the moduli space of holomorphic curves, we have to consider nodal curves.
On finiteness and rigidity of jholomorphic curves in. Its applications include many key results in symplectic topology. Jholomorphic curves and symplectic topology american. Differential geometry symplectic geometry, contact geometry gromovwitten invariants, quantum cohomology, frobenius manifolds. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. 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. Holomorphic curves in symplectic geometry it seems that youre in usa. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from jholomorphic map theory, that is, jholomorphic curves minimize the difference between the quantum covariance matrix determinant. Report jholomorphic curves and symplectic topology your name. It is related to the theory of dynamical systems and via holomorphic curves to algebraic geometry. The theory of jholomorphic 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. Its mathematical applications include many key results in symplectic topology. A parametrized pseudo holomorphic jcurve in an almost complex manifold is. Applications of pseudo holomorphic curves to symplectic topology. Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds. 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. Jholomorphic curves and symplectic topology pdf free. Compactness for punctured holomorphic curves cieliebak, k. Jholomorphic curves and symplectic topology semantic scholar. Introduction applications of pseudo holomorphic curves to symplectic topology. Symplectic topology and geometric quantum mechanics asu. We show that this satisfies the theorem of desargues if and only if j is isomorphic to the standard complex structure. Symplectic topology is a subfield of symplectic geometry, in which global properties of symplectic.
Lectures on symplectic manifolds download ebook pdf. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from j holomorphic map theory, that is, j holomorphic curves minimize the difference between the quantum covariance matrix determinant. Download j holomorphic curves and symplectic topology or read online here in pdf or epub. Jholomorphic curves and symplectic topology request pdf. Please click button to get j holomorphic curves and symplectic topology book now. J holomorphic curves and symplectic topology dusa mcduff, dietmar salamon download bok. Lectures on pseudoholomorphic curves and the symplectic isotopy problem bernd siebert and gang tian abstract. In mathematics, specifically in topology and geometry, a pseudoholomorphic curve or j holomorphic curve is a smooth map from a riemann surface into an almost complex manifold that satisfies the cauchyriemann equation. P pansu, pseudoholomorphic curves in symplectic manifolds, from. The structure of pseudoholomorphic subvarieties for. Jholomorphic curves and symplectic topology dusa mcduff. J holomorphic curves and symplectic topology download.
Jholomorphic curves in symplectic topology manabu akaho tokyo metropolitan university. Jholomorphic curves and quantum cohomology dusa mcduff. J holomorphic curves and symplectic topology second edition erratum dusa mcdu barnard college columbia university dietmar a. Introduction applications of pseudoholomorphic curves to symplectic topology. J holomorphic curves and symplectic topology download ebook. This is explained for example in mcduffsalomons j holomorphic curves in symplectic topology, in one of the first sections. Introduced in 1985 by mikhail gromov, pseudoholomorphic curves have since revolutionized the study of symplectic manifolds.
Full text views reflects the number of pdf downloads, pdfs. In particular if it is a closed curve it is minimizing in its homology class. The purpose of these notes is a more selfcontained presentation of the results of the authors in siti3. Get your kindle here, or download a free kindle reading app. Since the first edition of this book appeared in 2004, symplectic geometry has developed apace. Jholomorphic curves and symplectic topology by dusa.
Symplectic geometry on moduli spaces of jholomorphic curves j. Lectures on pseudo holomorphic curves and the symplectic isotopy problem bernd siebert and gang tian abstract. Mcduffsalamons book j holomorphic curves and symplectic topology, second edition. Jholomorphic curves and symplectic topology 2nd dusa. The projective plane, jholomorphic curves and desargues. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Jholomorphic curves and symplectic topology mathematical. Click download or read online button to get lectures on symplectic manifolds book now. Symplectic geometry on moduli spaces of jholomorphic curves.
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