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

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) (\(\mathbb{C}P^2\sharp\mathbb{C}P^2\))-bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (2) q...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Author: Hasui, Sho
Format: Article
Language:English
Subjects:
Bundling
Homology
Manifolds
Rings (mathematics)
Online Access:Get full text
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Summary:The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (1) (\(\mathbb{C}P^2\sharp\mathbb{C}P^2\))-bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (2) 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1409.7980