Speaker: Dusa McDuff (Columbia University)
Title: Constructing the Gromov-Witten virtual moduli cycle
Abstract: In Gromov-Witten theory one has a compact space X of holomorphic curves that in very good situations is an oriented smooth manifold of dimension d, but usually is not. One wants to "approximate" X by a nicer space X^[vir], called the virtual moduli cycle, that plays the role of the d-dimensional fundamental homology class. Then, via intersection theory, one can use X^[vir] to count the number of curves through a given set of homological constraints, the first step in Gromov-Witten theory. This talk will try to explain in an elementary way some of the issues (both analytical and topological) that come up in the construction of X^[vir], showing one way to resolve them. Though mostly based on the recent paper by Wehrheim and McDuff, the talk will also discuss new work on how to deal with nontrivial isotropy groups.