| Description |
1 online resource (230 pages) |
| Series |
Memoirs of the American Mathematical Society ; v. 248 |
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Memoirs of the American Mathematical Society.
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| Contents |
Cover; Title page; Chapter 1. Introduction and Main Results; 1.1. The Space Z of Stable Curves; 1.2. The Bundle W; 1.3. Fredholm Theory; 1.4. The GW-invariants; Chapter 2. Recollections and Technical Results; 2.1. Deligne-Mumford type Spaces; 2.2. Sc-smoothness, Sc-splicings, and Polyfolds; 2.3. Polyfold Fredholm Sections of Strong Polyfold Bundles; 2.4. Gluings and Anti-Gluings; 2.5. Implanting Gluings and Anti-gluings into a Manifold; 2.6. More Sc-smoothness Results.; Chapter 3. The Polyfold Structures; 3.1. Good Uniformizing Families of Stable Curves |
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3.2. Compatibility of Good Uniformizers3.3. Compactness Properties of (\cg,\cg'); 3.4. The Topology on ; 3.5. The Polyfold Structure on the Space ; 3.6. The Polyfold Structure of the Bundle → ; Chapter 4. The Nonlinear Cauchy-Riemann Operator; 4.1. Fredholm Sections of Strong Polyfold Bundles; 4.2. The Cauchy-Riemann Section: Results; 4.3. Some Technical Results; 4.4. Regularization and Sc-Smoothness of \ov{∂}_{ }; 4.5. The Filled Section, Proof of Proposition 4.8; 4.6. Proofs of Proposition 4.23 and Proposition 4.25; Chapter 5. Appendices; 5.1. Proof of Theorem 2.56 |
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5.2. Proof of Lemma 3.45.3. Linearization of the CR-Operator; 5.4. Consequences of Elliptic Regularity; 5.5. Proof of Proposition 4.11; 5.6. Banach Algebra Properties; 5.7. Proof of Proposition 4.12; 5.8. Proof of Proposition 4.16; 5.9. Proof of Lemma 4.19; 5.10. Orientations for Sc-Fredholm Sections; 5.11. The Canonical Orientation in Gromov-Witten Theory; Bibliography; Index; Back Cover |
| Summary |
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 polyf |
| Notes |
Print version record |
| Subject |
Symplectic geometry.
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Gromov-Witten invariants.
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Gromov-Witten invariants
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Symplectic geometry
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| Form |
Electronic book
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| Author |
Wysocki, K
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Zehnder, E
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| ISBN |
9781470440602 |
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1470440601 |
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