Holomorphic Curves in Symplectic Geometry (Progress in Mathematics (Birkhauser Boston))

Cover of: Holomorphic Curves in Symplectic Geometry (Progress in Mathematics (Birkhauser Boston)) |

Published by Birkhauser .

Written in English

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Subjects:

  • Symplectic manifolds,
  • Differential Geometry,
  • Mathematics,
  • Science/Mathematics,
  • Geometry - Differential,
  • Holomorphic functions

Edition Notes

Book details

ContributionsMichele Audin (Editor), Jacques Lafontaine (Editor)
The Physical Object
FormatHardcover
Number of Pages328
ID Numbers
Open LibraryOL8074258M
ISBN 100817629971
ISBN 109780817629977

Download Holomorphic Curves in Symplectic Geometry (Progress in Mathematics (Birkhauser Boston))

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. Buy this book. eB19 €. price for Spain Holomorphic Curves in Symplectic Geometry book Buy eBook. ISBN Digitally watermarked, DRM-free. Included format: PDF. ebooks can be used on all reading devices. Holomorphic Curves in Symplectic Geometry.

Editors (view affiliations) Michèle Audin; Jacques Lafontaine; Book. Citations; Search within book. Front Matter.

Pages i-xi. PDF. Introduction: Applications of pseudo-holomorphic curves to symplectic topology. Introduction Applications of pseudo-holomorphic curves to symplectic topology.

Holomorphic Curves in Symplectic Geometry by Michele Audin,available at Book Depository with free delivery worldwide. 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 problems.

Rational curves on holomorphic symplectic fourfolds Brendan Hassett and Yuri Tschinkel March 1 Introduction One of the main problems in the theory of irreducible holomorphic sym-plectic manifolds is the description of the ample cone in the Picard group.

The goal of this paper is to formulate explicit Hodge-theoretic criteria for. J Holomorphic Curves And Symplectic Topology by Dusa McDuff, J Holomorphic Curves And Symplectic Topology Books available in PDF, EPUB, Mobi Format. Download J Holomorphic Curves And Symplectic Topology books, This second edition continues to serve as the definitive source of information about some areas of differential topology ($J$-holomorphic curves) and applications to quantum cohomology.

The main goal of the book. The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves.

Warm up: Holomorphic curves in Cn The main subject of these notes is a certain interplay between symplectic struc-tures and complex (or rather almost complex) structures on smooth manifolds.

To illustrate the connection, we consider first the special case of holomorphic curves in Cn. If U ⊂ Cm is an open subset and u: U → Cn is a smooth map, we say that uis. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve : Springer International Publishing.

J-holomorphic Curves and Symplectic Topology - Dusa McDuff, Dietmar Salamon - Google Books. The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory.

holomorphic curves with boundary, but aimed to make Holomorphic Curves in Symplectic Geometry book for this by devoting the last third of the book to punctured holomorphic curves, a topic on which there are still very few available expositions aimed at graduate students.

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 Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including applications to Lagrangian embeddings problems.

The latter definition appears in Jason Lotay and Tommaso Pacini's article "Complexified diffeomorphism groups, totally real submanifolds and Kähler-Einstein geometry" and in section of Gromov's "Partial differential relations" and his "Pseudo holomorphic curves in symplectic manifolds.".

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. submanifolds give rise to foliations by J-holomorphic curves that determine the global structure of a symplectic manifold.

In our setting, the symplectic submanifolds feeding into McDuff’s technique are the pages of a planar spinal open book on the boundary of a symplectic filling, and the resulting J. Of course, on surfaces curves and divisors are equivalent.

In higher dimensions we can seek characterizations of both the e ective curves and the e ective divisors.

Thesis Let Xbe an irreducible holomorphic symplectic manifold of dimension 2n. There is a universal constant c X 2Q >0 depending. J-holomorphic curves and quantum cohomology Dusa McDuff and Dietmar Salamon $J$-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.

In a joint paper with Sam Lisi and Jeremy Van Horn-Morris, we proved that for "most" contact 3-manifolds admitting spinal open books with genus zero pages, all possible symplectic fillings come from Lefschetz fibrations whose fibers are J-holomorphic curves, including finitely.

This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details.

Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in MathematicsSpringer-Verlag. Note: the university library has this text available as an e-book here.

J-holomorphic curves: D. McDuff, D. Salamon, J-holomorphic curves and symplectic topology, AMS Colloquium Publ. 52. Lectures on Symplectic Geometry Ana Cannas da Silva1 revised January Published by Springer-Verlag as gave the subject a whole new set of tools: pseudo-holomorphic curves.

Gromov also first showed that important results from complex K¨ahler geometry remain true in the. The theory of \(J\)-holomorphic curves has been of great importance since its introduction by Gromov in In mathematics, its applications include many key results in symplectic topology.

It was also one of the main inspirations for the creation of Floer homology. Author: Yakov Eliashberg Publisher: American Mathematical Soc.

ISBN: Size: MB Format: PDF View: Get Books. Symplectic Geometry And Topology Symplectic Geometry And Topology by Yakov Eliashberg, Symplectic Geometry And Topology Books available in PDF, EPUB, Mobi Format. Download Symplectic Geometry And Topology books, Symplectic geometry has its.

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 Tσ. Symplectic Geometry And Topology Symplectic Geometry And Topology by Yakov Eliashberg.

Download it Symplectic Geometry And Topology books also available in PDF, EPUB, and Mobi Format for read it on your Kindle device, PC, phones or tablets. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.

J-holomorphic Curves and Symplectic Topology, by Dusa McDuff and Dietmar Salamon. An Introduction to Contact Topology, by Hansjorg Geiges Course Overview: Symplectic geometry is a central topic in mathematics with connections to algebraic geometry, differential geometry, complex geometry and topology.

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.

SYMPLECTIC TOPOLOGY AND HOLOMORPHIC CURVES, WINTERSEMESTER –, HU BERLIN 3 2. Basics on symplectic manifolds () Topics and reading. The Moser deformation trick is covered in [Wena, §], and you’ll find a more comprehensive discussion (including complete proofs of the Moser stability and Lagrangian.

As the authors of this book explain, J-holomorphic curves are a generalization of holomorphic curves the latter of which solve the Cauchy-Riemann equations. The Cauchy-Riemann equations are replaced by an expression involving the differentials of a map of a Riemann surface into a closed symplectic manifold M and what is called an `almost complex structure' J on M, which has the property that J^2 = Cited by: 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 cohomology.

The last chapter sketches some. [10] M. Audin and J. Lafontaine Editors, Holomorphic curves in symplectic geometry, Progress in Math-ematics, vol.

Birkh¨auser Verlag, Basel, MR 95i [11] Mich`ele Audin, The topology of torus actions on symplectic manifolds, Progress in Mathematics, vol. 93, Birkh¨auser Verlag, Basel, MR 92m J-holomorphic curves and symplectic topology by Dusa McDuff, Share this book. Facebook. Twitter. Pinterest.

Embed. Edit. Last edited by LC Bot. Pseudoholomorphic curves, Differential geometry -- Symplectic geometry, contact geometry -- Gromov-Witten invariants. See e.g. McDuff-Salamon, J-holomorphic Curves and Symplectic Topology, second edition, (which below I will call "big McDuff-Salamon"), Section Statement of McDuff's theorem on symplectic embeddings of four-dimensional ellipsoids.

See e.g. this survey article. Discussed the functor from differential topology to symplectic geometry. Books Here is the revised text of the book "J-holomorphic curves and Quantum Homology" (AMS Lecture Notes, ) that I wrote with Salamon.

This book is the (short!) first version of "J-holomorphic curves and Symplectic Topology" (AMS ). It contains a few mistakes and many omissions which are detailed in this Commentary of October In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology.

Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. The main references for this course are the following two books. We will also be discussing some topics which are not in either of these books, particularly in regard to holomorphic curve techniques, and I will give references for those as we go along.

Cannas da Silva, Lectures on Symplectic Geometry, authorized free download here. This book. 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. Gromov, Pseudo-holomorphic curves in symplectic manifolds. Audin-Lalonde-Polterovich, Symplectic rigidity: Lagrangian submanifolds.

Wendl, Lectures on holomorphic curves. Sandon, Generating functions in symplectic topologySome other books on basic symplectic geometry.

McDuff-Salamon, Introduction to Symplectic Topology. $\begingroup$ 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.On the symplectic side, this category is the Fukaya category, encoding counts of holomorphic curves into X.

The invariants obtained from the study of the holomorphic curve equation, whose first appearance in symplectic geometry is due to Misha Gromov, are very powerful yet difficult to compute; the good news is that recent advances in the.One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces.

The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new.

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