Guangbo Xu's Seminar

Curve counting invariants such as Gromov-Witten invariants are rational numbers in general because they are essentially certain orbifold Euler characteristics. In 1997 Fukaya-Ono proposed that by using the complex nature of the pseudoholomorphic curve equation one can extract integer invariants. In 2022 joint with S. Bai, we worked out the details following Fukaya-Ono's original idea and an important subsequent development by B. Parker. In this lecture I will talk about some of the details of this method which is called by us the FOP perturbation scheme. I will also talk about the multiplicative property of FOP perturbations which is necessary for applying to Floer theory.