Volume 17, issue 1 (2017)

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

Sho Hasui

Algebraic & Geometric Topology 17 (2017) 25–64
Abstract

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (i) $\left(ℂ\phantom{\rule{0.3em}{0ex}}{P}^{2}#ℂ\phantom{\rule{0.3em}{0ex}}{P}^{2}\right)$–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.

Keywords
quasitoric manifold, toric topology
Mathematical Subject Classification 2010
Primary: 57R19, 57S25