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

Ebook Details


H. Hofer, K. Wysocki, E. Zehnder

Year 2017
Pages 218
Publisher Amer Mathematical Society
Language en
ISBN 9781470422035
File Size 1.78 MB
File Format PDF
Download Counter 105
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Ebook Description

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.