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The homotopy classification of four-dimensional toric orbifolds

Published online by Cambridge University Press:  25 May 2021

Xin Fu
Affiliation:
Department of Mathematics, Ajou University, Suwon 16499, Republic of Korea ([email protected])
Tseleung So
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada ([email protected])
Jongbaek Song
Affiliation:
School of Mathematics, KIAS, Seoul 02455, Republic of Korea ([email protected])

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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