The Jones polynomial conjecture for detecting causality

Let $X$ be a $(2+1)$-dimensional globally hyperbolic spacetime with Cauchy surface $\Sigma$ not homeomorphic to $S^2$ or $\mathbb{R}P^2$. The Jones polynomial is considered as an invariant of the links formed by the skies of events in $X$.

Jones polynomial conjecture. The Jones polynomial detects causality between any two events in $X$.

The paper motivates this conjecture by empirical evidence and by topological restrictions on links of skies. It proves that the Conway polynomial does not detect causality in the stated setting, while the Jones-polynomial assertion remains open in the source.