Topological classification conjecture for the underlying space of the orbifold $\calO$

Let $\calO$ be an orbifold as in Theorem, and let $|\calO|$ denote its underlying topological space. Let $\CP^2[\lambda]$ denote the weighted projective plane, with underlying space $|\CP^2[\lambda]|$.

Topological classification conjecture for $|\calO|$. The underlying space $|\calO|$ is homeomorphic to either

$$S^4$$

or

$$|\CP^2[\lambda]|.$$

The preceding discussion derives the two possibilities from the isotropy cases $G_p=S^1$ and $G_p=\bbZ_q$. The source supplies no evidence that this conjectural classification has been proved or disproved.