Applications of Polyfold Theory I : The Polyfolds of Gromov-Witten Theory (Memoirs of the American Mathematical Society)

Hofer, H./ Wysocki, K./ Zehnder, E.

American Mathematical Society（2017/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 218 p.
• 言語 ENG
• 商品コード 9781470422035
• DDC分類 516.36

Full 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.

Contents

Introduction and main results
Recollections and technical results
The polyfold structures
The nonlinear Cauchy-Riemann operator
Appendices
Bibliography
Index.