Detecting Causality by Using Alexander Quandles and Alexander-Conway Polynomial
Keywords:
Causality, Alexander Quandles, Alexander-Conway PolynomialAbstract
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.
References or Bibliography
[Ame07] Kheira Ameur. Polynomial Quandle Cocycles, Their Knot Invariants
and Applications. PhD thesis, University of South Florida, 2007.
[AS21] Samantha Allen and Jacob H. Swenberg. Do link polynomials detect
causality in globally hyperbolic spacetime? Journal of Mathematical
Physics, 62(3):032503, 2021.
[CN10] Vladimir Chernov and Stefan Nemirovski. Legendrian links, causal-
ity, and the low conjecture. Geometric and Functional Analysis,
(5):1320–1333, 2010.
[Cro04] Peter Cromwell. Knots and Links. Cambridge University Press, 2004.
[Joy82] David Joyce. A classifying invariant of knots, the knot quandle. Jour-
nal of Pure and Applied Algebra, 23(1):37–65, 1982.
[Mat84] Matveev. Distributive groupoids in knot theory. Mathematics of the
USSR-Sbornik, 47(1):73–83, 1984.
[Nel] Sam Nelson. Quandles and racks. https://www1.cmc.edu/pages/
faculty/VNelson/quandles.html.
[VC20] Ina Petkova Vladimir Chernov, Gage Martin. Khovanov homology and
causality in spacetime. Journal of Mathematical Physics, 61(2):022503,
Downloads
Posted
License
Copyright (c) 2023 Nikhila Pasam
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The copyright holder for this article has granted JSR.org a license to display the article in perpetuity.