Counting J-holomorphic discs plays an essential role in Floer theory and mirror symmetry. However, the moduli space of J-holomorphic discs is in general singular due to the bubbling phenomenon. Fukaya and Ono constructed a coordinate system called Kuranishi structure to describe the orbifold structure of the moduli space and achieve the transversality. We will discuss its application for the Lagrangian Floer theory.

 

Reference:

 

Lagrangain Intersection Floer theory,  Anomaly and Obstruction