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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 $C^n(m)^*$, when $n>3$ or $m-n=3$. Besides, we classify small covers, the real version of quasitoric manifolds, over all dual cyclic polytopes.
A quasitoric manifold is a smooth manifold with a locally standard torus action for which the orbit space is identified with a simple polytope. For a class of topological spaces, the class is called strongly cohomologically rigid if any isomorphism o
The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) ($mathbb{C}P^2sharpmathbb{C}P^2$)-bundle type quasitoric manifolds are weakly equivariantly homeomorphic if the
We show a homotopy decomposition of $p$-localized suspension $Sigma M_{(p)}$ of a quasitoric manifold $M$ by constructing power maps. As an application we investigate the $p$-localized suspension of the projection $pi$ from the moment-angle complex o
It is proved that if two quasitoric manifolds of dimension $le 2p^2-4$ for a prime $p$ have isomorphic cohomology rings, then they have the same $p$-local stable homotopy type.
We give a new proof of a result of Lazarev, that the dual of the circle $S^1_+$ in the category of spectra is equivalent to a strictly square-zero extension as an associative ring spectrum. As an application, we calculate the topological cyclic homol