Introduction to Virtual Neighborhood Technique

Bohui Chen

Given an Banach bundle E over a Banach manifold B with a Fredholm type section s, suppose that the zero set M of the section is compact. We explain how to define the Euler class for such a system by using virtual neighborhood technique. Then I may talk about how the method can be applied to more general cases in terms of groupoids.

http://scgp.stonybrook.edu/video_portal/video.php?id=1571

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