Skip to Main Content

AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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)
Published electronically: March 20, 2017
Keywords: sc-smoothess, polyfolds, polyfold Fredholm sections, GW-invariants
MSC: Primary 58B99, 58C99, 57R17

View full volume PDF

View other years and numbers:

Table of Contents


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


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.

References [Enhancements On Off] (What's this?)