On the classification of quasitoric manifolds over dual cyclic polytopes

Abstract

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 $C^n{\left(m\right)}^{\ast }$ when $n>3$ or $m-n=3$. Additionally, we classify small covers, the “real version” of quasitoric manifolds, over all dual cyclic polytopes.