Construction of symplectic field theory and smoothness of Kuranishi structure

2019/06/19 Wed 16:30 - 17:30
Room 110, RIMS
Suguru Ishikawa
Kyoto University, RIMS

Symplectic field theory (SFT) is a generalization of Gromov-Witten invariant and Floer homology for contact maniflods and symplectic cobordisms between them. It was introduced by Eliashberg, Givental and Hofer around 2000, and its algebraic structure was well studied by them. However, for a long time, it was a difficult problem to construct SFT by counting pseudoholomorphic curves.
Recently, I succeeded in its construction by using Kuranishi theory, a theory developed by Fukaya and Ono for the construction of Gromov-Witten inavriant and Floer homology for general symplectic manifolds. In this talk, I explain about this work. Especially, I will talk about smoothness of Kuranishi structure.