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An Introduction To Compactness Results In Symplectic Field Theory

Author: Casim Abbas
Publisher: Springer Science & Business Media
ISBN: 3642315437
Size: 52.31 MB
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This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.

Bordered Heegaard Floer Homology

Author: Robert Lipshitz
Publisher: American Mathematical Soc.
ISBN: 1470428881
Size: 79.57 MB
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The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

New Perspectives And Challenges In Symplectic Field Theory

Author: Miguel Abreu
Publisher: American Mathematical Soc.
ISBN: 0821870432
Size: 44.58 MB
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This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.

Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory

Author: H. Hofer
Publisher: American Mathematical Soc.
ISBN: 1470422034
Size: 67.88 MB
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In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.

J Holomorphic Curves And Symplectic Topology

Author: Dusa McDuff
Publisher: American Mathematical Soc.
ISBN: 0821887467
Size: 41.79 MB
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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 is to establish the fundamental theorems of the subject in full and rigorous detail. It may also serve as an introduction to current work in symplectic topology. The second edition clarifies various arguments, includes some additional results, and updates the references to recent developments.

Geometry Topology

Size: 22.59 MB
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.