Northern California Symplectic Geometry Seminar: Floer Memorial Lecture: Constructing Relative Fundamental Classes

Seminar | October 2 | 4-5 p.m. | 748 Evans Hall

 Eleny Ionel, Stanford

 Department of Mathematics

Families of moduli spaces in symplectic Gromov-Witten theory and gauge theory are often manifolds that have "thin" compactifications, in the sense that the boundary of the generic fiber has codimension at least two. In this talk I will discuss a notion of a relative fundamental class for such thinly compactified families. It associates to each fiber, regardless whether it is regular or not, an element in its Cech homology in a way that is consistent along paths. We give several examples of this construction, discuss some of its properties, and its benefits. This talk is based on joint work with Tom Parker.