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toric orbifold

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

The homotopy classification of four-dimensional toric orbifolds
Part of
- Homotopy theory
- Differential topology
Xin Fu, Tseleung So, Jongbaek Song
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 3 / June 2022

Published online by Cambridge University Press:

25 May 2021, pp. 626-648

Print publication:

June 2022
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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.