Seminar

Often in symplectic topology we wish to constrain moduli spaces of pseudoholomorphic curves to consist of those curves satisfying intersection conditions with submanifolds. For example, any fiber product of moduli spaces over evaluation maps at marked points is an example of such a constraint. The evaluation maps will usually not be transverse on the moduli spaces, however they extend to the ambient polyfold and here they are transverse. Using this transversality, we explain how to construct the constrained polyfold and the constrained sc-Fredholm section. This provides an abstract tool to regularize constrained moduli spaces. We discuss an example with Gromov-Witten moduli spaces, and a construction of the Piunikhin-Salamon-Schwarz maps.