Topological orbifold models and quantum cohomology rings

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP¹ by the dihedral groupD₄, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP¹ orbifolds. We then considerCP²/D₄, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Supported in part by Fannie and John Hertz Foundation