Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure

Kenji Fukaya

I will start reviewing the previous talk about the local `universal’ family of deformation of Riemann surface plus curves. Then I will include two new points to discuss. We include the case when there is a finite group of symmetry of the pair (of marked Riemann surfact plus map). We study the case when the symmetry is infinite after forgetting the maps. Then I will define the notion of Kuranish chart (in the case when there is a finite group of symmetry also.) If time allows I explain the notion of stable map (where singularity (node) may exists in the source curve) and gives a summary of the way how to construct a local Kuranishi chart in such a case. (The detailed study of that case will be discussed later.)

http://scgp.stonybrook.edu/video_portal/video.php?id=1560

Simons- Program: Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology