Topological classification of quasitoric manifolds with 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.We classify quasitoric manifolds with second Betti number β 2 = 2 topologically.Interestingly, they are distinguished by their cohomology rings up to homeomorphism.