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.

中文翻译：

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四维复曲面环的同伦分类

让X是一个 4 维复曲面 orbifold。如果$H^{3}(X)$有一个非平凡的奇数初级扭转，那么我们证明X是同伦等价于摩尔空间和 CW 复形的楔形。作为推论，给定两个在上同调中没有 2-torsion 的 4 维复曲面 orbifold，我们证明它们具有相同的同伦类型，当且仅它们的积分上同调环是同构的。