Mukai Flop and Ruan Cohomology

Suppose that two compact manifolds $X,X^{\mathrm{\prime }}$ are connected by a sequence of Mukai flops. In this paper, we construct a ring isomorphism between cohomology ring of $X$ and $X^{\mathrm{\prime }}$. Using the local mirror symmetry technique, we prove that the quantum corrected products on $X,X^{\mathrm{\prime }}$ are the ordinary intersection products. Furthermore, $X,X^{\mathrm{\prime }}$ have isomorphic Ruan cohomology. i.e. we proved the cohomological minimal model conjecture proposed by Ruan.