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Thursday, April 30, 2020 | History

3 edition of Holomorphic curves in symplectic geometry found in the catalog.

Holomorphic curves in symplectic geometry

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  • 28 Currently reading

Published by Birkhäuser in Basel, Boston .
Written in English

    Subjects:
  • Symplectic manifolds.,
  • Holomorphic functions.

  • Edition Notes

    Includes bibliographical references and index.

    StatementMichèle Audin, Jacques Lafontaine, editors.
    SeriesProgress in mathematics ;, v. 117, Progress in mathematics (Boston, Mass) ;, v. 117.
    ContributionsAudin, Michèle., Lafontaine, J. 1944 Mar. 10-
    Classifications
    LC ClassificationsQA649 .H65 1994
    The Physical Object
    Paginationxi, 328 p. :
    Number of Pages328
    ID Numbers
    Open LibraryOL1436474M
    ISBN 100817629971, 3764329971
    LC Control Number93048724

    August 4 to 9, at the American Institute of Mathematics, Palo Alto, California. organized by Yasha Eliashberg and John Etnyre. This workshop, sponsored by AIM and the NSF, will be devoted to the development of holomorphic curve techniques in contact geometry and advent of holomorphic curve techniques in contact topology, as exemplified in Symplectic Field Theory (SFT), .


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Holomorphic curves in symplectic geometry Download PDF EPUB FB2

This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings : Hardcover.

Holomorphic Curves in Symplectic Geometry. Editors (view affiliations) Michèle Audin; Jacques Lafontaine; Book. Citations; Applications of pseudo-holomorphic curves to symplectic topology.

Basic symplectic geometry. Front Matter. Pages PDF. An introduction to symplectic geometry. Augustin Banyaga. Pages Symplectic and. Holomorphic Curves in Symplectic Geometry. Editors: Audin, Michele, Lafontaine, Jacques (Eds.) Introduction Applications of pseudo-holomorphic curves to symplectic topology.

Pages Services for this Book. Download Product Flyer Download High-Resolution Cover. Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds.- 3 Proofs of the symplectic rigidity results.- 4 What is in the book and what is not.- 1: Basic symplectic geometry.- I An introduction to.

Deals with the pseudo-holomorphic curve methods in symplectic geometry. This book contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of. an invaluable reference for users. but for a first stab at j-holomorphic curves and applications in symplectic topology one might want to try the little version instead (same authors, title contains the words "quantum cohomology") - which as a bonus is available for free on at least one of the authors' website (i think).Cited by: 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 Brand: Springer International Publishing.

The five appendices of the book provide necessary background related to the classical theory of linear elliptic operators, Fredholm theory, Sobolev spaces, as well as a discussion of the moduli space of genus zero stable curves and a proof of the positivity of intersections of \(J\)-holomorphic curves in four-dimensional manifolds.

From symplectic geometry to symplectic topology 10 Contact geometry and the Weinstein conjecture 13 Symplectic fillings of contact manifolds 19 Chapter 2. Local properties 23 Almost complex manifolds and J-holomorphic curves 23 Compatible and tamed almost complex structures 27 Linear Cauchy-Riemann type operators File Size: 1MB.

For a more Lie-group focused account, you can try Robert Bryant's lectures on Lie groups and symplectic geometry which are available online here.

In the final lecture he describes the h-principle and others ideas of Gromov in symplectic geometry, like pseudo-holomorphic curves. 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.

The school, the book This book is based on lectures given by the authors of the various chapters in a three week long CIMPA summer school, held in Sophia-Antipolis (near Nice) in July The first week was devoted to the basics of symplectic and Riemannian geometry (Banyaga, Audin, Lafontaine, Gauduchon), the second was the technical one (Pansu, Muller, Duval, Lalonde and Sikorav).

The. From symplectic geometry to symplectic topology 10 Contact geometry and the Weinstein conjecture 13 Symplectic fillings of contact manifolds 19 Chapter 2. Fundamentals 25 Almost complex manifolds and J-holomorphic curves 25 Compatible and tame almost complex structures 29 Linear Cauchy-Riemann type operators 40 Cited by: 3 Pseudo-holomorphic curves The aim of this part is to study some of the important properties of the pseudo-holomorphiccurves.

Definition(Pseudo-holomorphiccurve). Let(M,J) beanalmostcomplexmanifold. A J-holomorphic curve in M is a smooth map σfrom a Riemann surface (i.e a surface withacomplexstructure)(S,j) to(M,J) suchthat: Tσ j= J TσFile Size: KB. J-holomorphic Curves and Symplectic Topology (2nd) Dusa McDuff, Dietmar Salamon.

Categories: Holomorphic Curves in Symplectic Geometry. Birkhäuser Basel. Jacques Lafontaine, Michèle Audin (auth.) You can write a book review and share your experiences.

Other readers will always be interested in your opinion of the books you've read. Bloggat om Holomorphic Curves in Symplectic Geometry Innehållsförteckning Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds.- 3 Proofs of the symplectic rigidity results.- 4 What is in the book.

Pseudo-holomorphic curves Almost complex and symplectic geometry. An almost complex structure on a manifold Mis a bundle endomorphism J: TM → TM with square −idT M. In other words, Jmakes TM into a complex vector bundle and we have the canonical decomposition TM⊗R C = T 1,0 M ⊕T 0,1 M = TM⊕TM into real and imaginary parts.

From symplectic geometry to symplectic topology 10 Contact geometry and the Weinstein conjecture 13 Symplectic fillings of contact manifolds 19 Chapter 2. Fundamentals 25 Almost complex manifolds and J-holomorphic curves 25 Compatible and tame almost complex structures 29 Linear Cauchy-Riemann type operators 41   So, what’s a J-holomorphic curve?Well, as the Preface to the first edition of the book under review states, it goes back to a paper by Mikhail Gromov, titled “Pseudo-holomorphic curves in symplectic manifolds,” and on p.3 of the book McDuff and Salamon give its definition as a (j,J)-holomorphic mapping from a Riemann surface (with j being — well, what else.

— its j-invariant) to. 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 Cauchy–Riemann uced in by Mikhail Gromov, pseudoholomorphic curves have since revolutionized the study of symplectic particular, they lead to the Gromov–Witten.

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate ctic 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 manifold.

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole.

Holomorphic curves in symplectic geometry, –, Progress in Mathematics, Birkhäuser, Basel,   The goal of the program is to explore different aspects of the theory of holomorphic curves and their interaction.

A special accent will be made on applications to Symplectic geometry in low-dimensional topology. The book can also serve as an introduction to current work in symplectic topology: there are two long chapters on applications, one concentrating on classical results in symplectic topology and the other concerned with quantum : $ Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in Hamilton’s equation.

It is related to the theory of dynamical systems and - via holomorphic curves – to algebraic geometry. Symplectic topology is a subfield of symplectic geometry, in which global properties of symplectic. Part 1.

Elementary symplectic geometry 7 Chapter 2. Symplectic linear algebra 9 1. Basic facts 9 2. Complex structure 13 Chapter 3. Symplectic differential geometry 17 1.

Moser’s lemma and local triviality of symplectic differential geometry 17 2. The groups Ham and Di f f. 21 Chapter 4. More Symplectic differential Geometry: Reduction and File Size: KB. 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.

$\begingroup$ It's unclear to me what you are looking for here, or what you know already. The question of how many holomorphic curves there are in a given homology class (with constraints possibly) is given by Gromov-Witten invariants. One possible option seems to be taking critial points off.

But then the immersion is not proper and the proof of the monotonicity formula seems to use properness. For example, the proof in the book "holomorphic curves in symplectic geometry" uses a compactly supported vector field. An holomorphic symplectic manifold X is a kähler manifold X with a holomorphic non degenerate closed form σ ∈ H0(X,Ω2 X) An irreducible holomorphic symplectic manifold X is compact and H0(X,Ω∗ X) = C[σ] (eq.

X is simply connected and = H0(X,Ω2 X)). Calabi-Yau: projective mfds with H0(X,Ω∗ X) = C+Cω, where ω is a generator File Size: KB. Pseudoholomorphic curves. Differential geometry -- Symplectic geometry, contact geometry -- Symplectic manifolds, general.

Differential geometry -- Symplectic geometry, contact geometry -- Gromov-Witten invariants, quantum cohomology, Frobenius manifolds. computing $\mathcal{M}(A, J_1)$ using techniques from algebraic geometry.

An important aspect of Gromov's use of almost complex structure and (pseudo)holomorphic. Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions.

Siefring's recent extension of the. 4. Symplectic fibrations 5. Hofer's geometry of Ham(M, ω) 6. C0-Symplectic topology and Hamiltonian dynamics.

Part II. Rudiments of Pseudoholomorphic Curves: 7. Geometric calculations 8. Local study of J-holomorphic curves 9. Gromov compactification and stable maps Fredholm theory Applications to symplectic topology.

References Index. Download Citation | Lectures on Holomorphic Curves in Symplectic and Contact Geometry | This is a set of expository lecture notes created originally for a graduate course on holomorphic curves Author: Chris Wendl.

The main focus of this workshop will be on holomorphic curve techniques in low-dimensional topology and symplectic geometry. The workshop is a part of the FRG: Collaborative Research: Topology and Invariants of Smooth 4-Manifolds. It is funded by NSF Focused Research Grant DMS J$-holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics.

Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds. Read "Symplectic Topology and Floer Homology: Volume 1, Symplectic Geometry and Pseudoholomorphic Curves" by Yong-Geun Oh available from Rakuten Kobo.

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology Brand: Cambridge University Press.

Symplectic geometry on moduli spaces of J-holomorphic curves J. Coffey, L. Kessler, and A. Pelayo´ Abstract Let (M;!) be a symplectic manifold, and a compact Riemann surface. We define a 2-form. S i() on the space S i() of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations.

of J-holomorphic curves and symplectic topology has now become routine and causes no confusion. This book begins with a sixteen-page overview of the subject of symplectic topology, the theory of J-holomor-phic curves, and its applications to symplectic topology, algebraic File Size: KB.Symplectic 4-manifolds The group of symplectomorphisms Hofer geometry Distinguishing symplectic structures Chapter Gluing The gluing theorem Connected sums of J-holomorphic curves Weighted norms Cutoff functions Construction of the gluing map J-holomorphic curves in symplectic geometry Janko Latschev Pleinfeld, September 25 – 28, Since their introduction by Gromov [4] in the mid’s J-holomorphic curves have been one of the most widely used tools in symplectic geometry, leading to the formulation of various theories (Gromov-Witten invariants, quantum co-Author: Janko Latschev.