On the classification of quasitoric manifolds over the dual cyclic polytopes

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