The simple polygon space conjecture

Let $S(n)$ be the connected component of the space of simple labeled $n$-gons modulo oriented similarity consisting of positively oriented polygons. As an open subset of $\mathbb{C}\mathbb{P}^{n-2}$, it is an analytic manifold. Simple polygon space conjecture. $S(n)$ is homeomorphic to $\mathbb{R}^{2n-4}$. This conjecture proposes a global Euclidean model for the moduli space of positively oriented simple polygons; the supplied source does not state whether it has been resolved.