Topological classification of quasitoric manifolds with the second Betti number 2

Abstract

A quasitoric manifold is a $2n$-dimensional compact smooth manifold with a locally standard action of an $n$-dimensional torus whose orbit space is a simple polytope. In this article, we classify quasitoric manifolds with the second Betti number $\beta_2=2$ topologically. Interestingly, they are distinguished by their cohomology rings up to homeomorphism.