On the classification of quasitoric manifolds over the 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 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 $C^n(m{)}^{\ast }$, when $n>3$ or $m-n=3$. Besides, we classify small covers, the "real version" of quasitoric manifolds, over all dual cyclic polytopes.

31 pages, 0 figure

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