The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (i) –bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (ii) quasitoric manifolds over 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.
"On the cohomology equivalences between bundle-type quasitoric manifolds over a cube." Algebr. Geom. Topol. 17 (1) 25 - 64, 2017. https://doi.org/10.2140/agt.2017.17.25