Joint IAS/Princeton University Symplectic Geometry Seminar

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.