Dong Youp Suh

Classification of quasitoric manifolds with the second Betti number equal to 2 and cohomological rigidity problem

video: comming soon.
abstract:
In this talk we classify all quasitoric manifolds with the second Betti numbers equal to 2 up to homeomorphism. A quasitoric manifold is a topological analogue of a toric variety, which is a closed \(2n\) dimensional manifold with an n-dimensional torus action whose orbit space has the structure of a simple convex polytope of dimension \(n\). The orbit space of a quasitoric manifold with the second Betti number 2 is a product of two simplices. Using the classification result we can prove that any two quasitoric manifolds with the second Betti number 2 are homeomorphic if and only if there cohomology rings are isomorphic.