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Applications of Polyfold Theory I: The Polyfolds of Gromov–Witten Theory
About this Title
H. Hofer, Institute for Advanced Study, USA, K. Wysocki, Penn State University and E. Zehnder, ETH-Zurich,Switzerland
Publication: Memoirs of the American Mathematical Society
Publication Year:
2017; Volume 248, Number 1179
ISBNs: 978-1-4704-2203-5 (print); 978-1-4704-4060-2 (online)
DOI: https://doi.org/10.1090/memo/1179
Published electronically: March 20, 2017
Keywords: sc-smoothess,
polyfolds,
polyfold Fredholm sections,
GW-invariants
MSC: Primary 58B99, 58C99, 57R17
Table of Contents
Chapters
- 1. Introduction and Main Results
- 2. Recollections and Technical Results
- 3. The Polyfold Structures
- 4. The Nonlinear Cauchy-Riemann Operator
- 5. Appendices
Abstract
In this paper we 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 we shall use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.- F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki, and E. Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003), 799–888. MR 2026549, DOI 10.2140/gt.2003.7.799
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