On the classification of quasitoric manifolds over dual cyclic polytopes

For a simple n-polytope P, a quasitoric manifold over P is a 2n-dimensional smooth manifold with a locally standard action of an n-dimensional torus for which the orbit space is identified with P. This paper acheives the topological classification of quasitoric manifolds over the dual cyclic polytope C-n(m)* when n > 3 or m-n = 3. Additionally, we classify small covers, the "real version" of quasitoric manifolds, over all dual cyclic polytopes.