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The homotopy classification of four-dimensional toric orbifolds

Part of: Differential topology Homotopy theory

Published online by Cambridge University Press:  25 May 2021

Xin Fu ,
Tseleung So  and
Jongbaek Song Open the ORCID record for Jongbaek Song [Opens in a new window]
Xin Fu
Affiliation:
Department of Mathematics, Ajou University, Suwon 16499, Republic of Korea (xfu87@ajou.ac.kr)
Tseleung So
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada (tse.leung.so@uregina.ca)
Jongbaek Song
Affiliation:
School of Mathematics, KIAS, Seoul 02455, Republic of Korea (jongbaek@kias.re.kr)
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Abstract

Let X be a 4-dimensional toric orbifold. If $H^{3}(X)$ has a non-trivial odd primary torsion, then we show that X is homotopy equivalent to the wedge of a Moore space and a CW-complex. As a corollary, given two 4-dimensional toric orbifolds having no 2-torsion in the cohomology, we prove that they have the same homotopy type if and only their integral cohomology rings are isomorphic.

Keywords

Cohomological rigiditytoric orbifold

MSC classification

Primary: 57R18: Topology and geometry of orbifolds 55P15: Classification of homotopy type
Secondary: 55P60: Localization and completion
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 3 , June 2022 , pp. 626 - 648
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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