Virtual neighbourhood technique and its applications

Princeton/IAS Symplectic Geometry Seminar
Topic:Virtual neighbourhood technique and its applications
Speaker:Bai-Ling Wang
Affiliation:Australian National University
Date:Friday, March 28
Time/Room:1:30pm - 2:30pm/Fine 322, Princeton University

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.