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 beta(2) =2 topologically. Interestingly, they are distinguished by their cohomology rings up to homeomorphism.