Classification of quasitoric manifolds with the second Betti number
equal to 2 and cohomological rigidity problem
video: comming soon.
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.