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

Download or read book Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory written by H. Hofer and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.