Detecting Causality by Using Alexander Quandles and Alexander-Conway Polynomial

Abstract

The paper by Samantha Allen and Jacob H. Swenberg suggests that the Jones polynomial is likely able to detect causality in 2+1-dimension global hyperbolic spacetime; however, the Alexander-Conway polynomial cannot. The natural question that arises then is what extra information needs to be added to the Alexander-Conway polynomial so that it can also distinguish causality. In this paper, I used some of the Alexander Quandles for the connected sum of 2 Hopf links and the Allen-Swenberg link and obtained the result that it does not distinguish between the two links, so it cannot detect causality.