Quandles in Causality

Abstract

This paper aims to study the colorability of links proposed by Samantha Allen and Jacob H. Swenberg using the Alexander quandle. There are two examples of links which are important for the study of causality; Allen-Swenberg's paper shows that Jones Polynomial is most likely enough to distinguish causality in 2+1 dimensional globally hyperbolic spacetimes, but Alexander-Conway Polynomial is likely not enough. I have checked what extra information would plausibly be needed along with Alexander-Conway Polynomial to distinguish causality. I have used the Alexander Quandle by considering the set, Zn, integers modulo n, and an integer t co-prime to n, n being the element of the set of prime numbers. I have gotten that it does not distinguish the Allen-Swenberg examples, so it can not help distinguish causality