A pr 2 00 8 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 − z + t = 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 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.