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

Hasui, Sho

doi:10.2140/agt.2017.17.25

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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

DOI: 10.2140/agt.2017.17.25

Abstract

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (i) $(ℂ P^{2} # ℂ P^{2})$ –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

References

Publication

Received: 3 December 2014

Revised: 27 February 2016

Accepted: 9 July 2016

Published: 26 January 2017

Authors

Sho Hasui
Department of Mathematics, Faculty of Science Kyoto University Kitashirakawa Oiwake-cho, Sakyo-ku Kyoto 606-8502 Japan

Volume 17, issue 1 (2017)