Mukai Flop and Ruan Cohomology

Abstract

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