Contents

Idea

Symplectic field theory is a mathematical approach to Gromov-Witten invariants (and invariants in contact geometry and the relative invariants of Legendrean submanifolds (relative contact homology)) in the spirit of topological field theory. It has inspired to some extent Hofer’s generalized Fredholm theory on polyfolds.

References

• Yakov Eliashberg, Alexander Givental, Helmut Hofer, Introduction to symplectic field theory, math.SG/0010059
• wikipedia: Floer homology:symplectic field theory
• Oliver Fabert, Paolo Rossi, Topological recursion relations in the symplectic field theory of mapping tori and local symplectic field theory, arxiv/1109.0972