Virtual neighbourhood technique and its applications

Virtual neighbourhood technique and its applications

-
Bai-Ling Wang, Australian National University
Fine Hall 322

In this talk, I will explain the recent joint work with Bohui Chen and Anmin Li on virtual neighborhood techniques for a Fredholm system (B, E, S), where E is a Banach vector bundle over a Banach manifold B with a Fredholm section. Using the notion of virtual manifold theory developed by Chen and Tian, we associate a virtual system for the moduli space M=S^{-1}(0). As an application, we will show that the moduli space of stable maps in a closed symplectic manifold admits an orbifold virtual system with a canonical orientation in cohomology or in K-theory.