Low's conjecture on linked skies

Let $(X,g)$ be a globally hyperbolic $(2+1)$-dimensional spacetime whose smooth spacelike Cauchy surface has universal cover $\mathbb{R}^2$. The sky of an event is the sphere of light rays passing through that event.

Low Conjecture. The skies of causally related points in $X$ are topologically linked.

This conjecture was proven by Chernov and Nemirovski; the source says the result holds when the Cauchy surface is not homeomorphic to $S^2$ or $\mathbb{R}P^2$.