Singular symplectic flops and Ruan cohomology

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient Wr={(x,y,z,t)∣xy−z2r+t2=0}/μr(a,−a,1,0),r≥1, which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let XX and YY be two symplectic orbifolds connected by such a flop. We study orbifold Gromov–Witten invariants of exceptional classes on XX and YY and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.