Online Talk

The long-standing cohomological rigidity problem for toric manifolds asks whether the integral cohomology ring of a toric manifold determines its homotopy type. We construct two toric manifolds of complex dimension four that have isomorphic integral cohomology rings but are not homotopy equivalent, thereby giving a negative answer to this problem. We also construct a family of such examples. This is joint work with Xin Fu, Sergei O. Ivanov, and Yingxin Li.