Online Talk

The long-standing cohomological rigidity problem for toric manifolds asks whether the integral cohomology ring of a toric manifold determines its diffeomorphism type, homeomorphism type, or homotopy type. We construct two toric manifolds of complex dimension four whose integral cohomology rings are isomorphic but which are not homotopy equivalent, thereby giving a negative answer to this problem. This is joint work with Yingxin Li.