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Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory

H. Hofer Institute for Advanced Study, Princeton, New Jersey, USA
K. Wysocki Penn State University, State College, Pennsylvania, USA
E. Zehnder ETH-Zurich, Zurich, Switzerland
Available Formats:
Electronic ISBN: 978-1-4704-4060-2
Product Code: MEMO/248/1179.E
List Price: $75.00 MAA Member Price:$67.50
AMS Member Price: $45.00 Click above image for expanded view Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory H. Hofer Institute for Advanced Study, Princeton, New Jersey, USA K. Wysocki Penn State University, State College, Pennsylvania, USA E. Zehnder ETH-Zurich, Zurich, Switzerland Available Formats:  Electronic ISBN: 978-1-4704-4060-2 Product Code: MEMO/248/1179.E  List Price:$75.00 MAA Member Price: $67.50 AMS Member Price:$45.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2482017; 218 pp
MSC: Primary 58; 57;

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.

• Chapters
• 1. Introduction and Main Results
• 2. Recollections and Technical Results
• 3. The Polyfold Structures
• 4. The Nonlinear Cauchy-Riemann Operator
• 5. Appendices

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Volume: 2482017; 218 pp
MSC: Primary 58; 57;

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.

• Chapters
• 1. Introduction and Main Results
• 2. Recollections and Technical Results
• 3. The Polyfold Structures
• 4. The Nonlinear Cauchy-Riemann Operator
• 5. Appendices
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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