Published Paper Details:

This paper aims to verify the ability of the Takasaki quandles to distinguish between the Allen-Swenberg link and the connected sum of two Hopf links. The results obtained are hence suggestive of the extra information required for the Alexander Conway polynomial to distinguish causality in 2+1 globally hyperbolic space-times for all events when the Cauchy surface has $mathbb R^2$ for the universal cover. The given quandle was tested for all primes under 50 to check whether the Takasaki quandle modular prime is able to provide a solution that may suggest causality. As the number of homomorphisms given by the Takasaki quandle for all primes for the Allen-Swenberg Link is equal to the number of homomorphisms of the connected sum of two Hopf links. As the links are found to not be distinguishable from one another, the Takasaki Quandle hence provides the information that it can not be utilised to obtain the extra information required for the Alexander Conway polynomial to distinguish causally related events in this particular example.