Detecting Causality with Symplectic Quandles

Abstract: We investigate the capability of Symplectic quandles to detect causality for (2+1)-dimensional globally hyperbolic spacetimes (X). Allen and Swenberg showed that Alexander-Conway polynomial is insufficient to distinguish connected sum of two Hopf links from the links in the family of Allen-Swenberg 2-sky like links, suggesting that it can not always detect causality in X. We find that symplectic quandles, combined with Alexander-Conway polynomial, can distinguish these two type of links, thereby suggesting their ability to detect causality in X. The fact that symplectic quandles can capture causality in the Allen-Swenberg example is intriguing since the theorem of Chernov and Nemirovski, which states that Legendrian linking equals causality, is proved using Contact Geometry methods.