On the cohomology equivalences between bundle-type quasitoric manifolds over a cube

Abstract

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (i) $\left(ℂP^2\#ℂP^2\right)$–bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (ii) quasitoric manifolds over $I^3$ are homeomorphic if their cohomology rings are isomorphic. In the latter case, there are only four quasitoric manifolds up to weakly equivariant homeomorphism which are not bundle-type.