Singular symplectic flops and Ruan cohomology

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient W r = { ( x , y , z , t ) ∣ x y − z 2 r + t 2 = 0 } / μ r ( a , − a , 1 , 0 ) , r ≥ 1 , which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let X and Y be two symplectic orbifolds connected by such a flop. We study orbifold Gromov–Witten invariants of exceptional classes on X and Y and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.