# Homotopy types of 4-dimensional toric orbifolds

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Tseleung So, University of Regina

Let $X$ be a 4-dimensional toric orbifold. It is known that $H^3(X)$ is trivial or a cyclic group. If it is $\mathbb{Z}/m$ and $m=2^sq$ for some odd number $q$, then we show that $X$ can be decomposed as a wedge of a mod-$q$ Moore space and a CW-complex whose cohomology group is $\Z/2^s$ at degree 3 and is $H^i(X)$ at degree $i\neq3$. As an application, we study the cohomology ridigity problem and prove that for any two 4-dimensional toric orbifolds whose degree 3 cohomology have no 2-torsion, they are homotopy equivalent if and only if their cohomology rings are isomorphic.