Abstract:

We will explain the construction of Kuranishi structure on moduli spaces of stable maps, following the motivation and abstract theory given in the lecture in October.  

 

References:

1. FOOO,  Kuranishi structure, Pseudo-holomorphic curve and virtual fundamental chain: Part I   arXiv:1503.0731 

(I will not cover Part II: arXiv:1704.01848 this time.)  

2. FOOO, Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks, I arXiv:1710.01459 

(I will not cover Part II: arXiv:1808.06106 this time.)  

 

NB: 

Part I:  Kuranishi structure on a single space => virtual fundamental cycle/chain construction of Kuranishi structure for a single moduli space 

Part II : a system of spaces of Kuranishi structures => algebraic structure construction of Kuranishi structures for a system of moduli spaces